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Author ID: trenkler.gotz Recent zbMATH articles by "Trenkler, Götz"
Published as: Trenkler, Götz; Trenkler, G.
Homepage: https://www.statistik.tu-dortmund.de/trenkler.html
External Links: MGP · Wikidata · ResearchGate · dblp · GND · IdRef
Documents Indexed: 160 Publications since 1976, including 6 Books
3 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 48 Co-Authors with 142 Joint Publications
862 Co-Co-Authors
all top 5

Serials

23 Linear Algebra and its Applications
14 International Journal of Mathematical Education in Science and Technology
9 Communications in Statistics. Theory and Methods
8 Linear and Multilinear Algebra
8 Statistical Papers
7 Applied Mathematics and Computation
7 Journal of Statistical Planning and Inference
6 Statistics
5 Sankhyā. Series A. Methods and Techniques
4 Statistica
4 Acta Applicandae Mathematicae
4 Discussiones Mathematicae. Probability and Statistics
3 Computational Statistics and Data Analysis
3 Test
3 Springer-Lehrbuch
2 Computers & Mathematics with Applications
2 Scandinavian Journal of Statistics
2 Annals of the Institute of Statistical Mathematics
2 Computational Statistics Quarterly
2 Communications in Statistics. Simulation and Computation
2 Statistische Hefte
2 Methods of Operations Research
2 The College Mathematics Journal
1 American Mathematical Monthly
1 Indian Journal of Pure & Applied Mathematics
1 Metrika
1 The Australian Journal of Statistics
1 Biometrical Journal
1 Industrial Mathematics
1 Journal of Econometrics
1 Journal of Multivariate Analysis
1 Sankhyā. Series B. Methodological
1 Statistica Neerlandica
1 Statistics & Probability Letters
1 SIAM Journal on Matrix Analysis and Applications
1 Economics Letters
1 Acta Mathematica Universitatis Comenianae. New Series
1 Journal of Statistical Computation and Simulation
1 Tatra Mountains Mathematical Publications
1 Discussiones Mathematicae. Algebra and Stochastic Methods
1 ELA. The Electronic Journal of Linear Algebra
1 Journal of Applied Mathematics and Decision Sciences
1 Australian & New Zealand Journal of Statistics
1 Discussiones Mathematicae. General Algebra and Applications
1 Acta Universitatis Apulensis. Mathematics - Informatics
1 International Journal of Information & Systems Sciences
1 Mathematical Systems in Economics
1 Journal of the Italian Statistical Society
1 ISRN Applied Mathematics
1 De Gruyter Lehrbuch

Publications by Year

Citations contained in zbMATH Open

120 Publications have been cited 1,194 times in 833 Documents Cited by Year
Core inverse of matrices. Zbl 1202.15009
Baksalary, Oskar Maria; Trenkler, Götz
253
2010
Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066
Trenkler, G.; Toutenburg, H.
72
1990
On a generalized core inverse. Zbl 1334.15009
Baksalary, Oskar Maria; Trenkler, Götz
57
2014
Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008
Liu, Shuangzhe; Trenkler, Götz
44
2008
On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. Zbl 0559.62054
Trenkler, Götz
34
1984
Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020
Gross, Jürgen; Trenkler, Götz
34
1999
On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004
Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz
33
2009
Generalized and hypergeneralized projectors. Zbl 0887.15024
Groß, Jürgen; Trenkler, Götz
32
1997
Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011
Baksalary, Jerzy K.; Trenkler, Götz
29
1991
Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023
Baksalary, Oskar Maria; Trenkler, Götz
28
2008
Quasi minimax-estimation in the linear regression model. Zbl 0635.62066
Trenkler, G.; Stahlecker, P.
28
1987
Mean square error matrix comparisons of estimators in linear regression. Zbl 0594.62075
Trenkler, Götz
19
1985
Further results on generalized and hypergeneralized projectors. Zbl 1151.15022
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz
17
2008
Revisitation of the product of two orthogonal projectors. Zbl 1167.15018
Baksalary, Oskar Maria; Trenkler, Götz
16
2009
Mean square error matrix improvements and admissibility of linear estimators. Zbl 0685.62052
Baksalary, Jerzy K.; Liski, Erkki P.; Trenkler, Götz
16
1989
Some further results on Hermitian-matrix inequalities. Zbl 0753.15014
Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz
15
1992
Column space equalities for orthogonal projectors. Zbl 1169.15007
Baksalary, Oskar Maria; Trenkler, Götz
15
2009
Biased estimators in the linear regression model. Zbl 0471.62070
Trenkler, Götz
14
1981
On disjoint range matrices. Zbl 1221.15005
Baksalary, Oskar Maria; Trenkler, Götz
13
2011
On the product of oblique projectors. Zbl 0929.15016
Groß, Jürgen; Trenkler, Götz
12
1998
The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056
Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim
11
2001
Characterizations of oblique and orthogonal projectors. Zbl 0827.62054
Trenkler, Götz
11
1994
A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165
Baksalary, Oskar Maria; Trenkler, Götz
11
2009
On angles and distances between subspaces. Zbl 1177.15024
Baksalary, Oskar Maria; Trenkler, Götz
11
2009
A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz
11
2003
A note on superiority comparisons of homogeneous linear estimators. Zbl 0523.62066
Trenkler, Götz; Trenkler, Dietrich
10
1983
On semi-orthogonality and a special class of matrices. Zbl 0949.15036
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
10
1999
Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004
Baksalary, Oskar Maria; Trenkler, Götz
10
2010
Full and partial minimax estimation in regression analysis with additional linear constraints. Zbl 0653.62053
Stahlecker, P.; Trenkler, G.
10
1988
Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061
Stahlecker, Peter; Trenkler, Götz
10
1993
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
10
2010
On \(k\)-potent matrices. Zbl 1283.15043
Baksalary, Oskar Maria; Trenkler, Götz
10
2013
Partial minimax estimation in regression analysis. Zbl 0647.62063
Hering, F.; Trenkler, G.; Stahlecker, P.
9
1987
Minimum mean square error estimation in linear regression. Zbl 0786.62068
Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz
9
1993
Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010
Baksalary, Oskar Maria; Trenkler, Götz
9
2009
Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093
Trenkler, G.; Toutenburg, H.
8
1992
Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. (Nichtparametrische statistische Methoden.) Zbl 0820.62031
Büning, Herbert; Trenkler, Götz
8
1994
Generalized mean squared error comparisons of biased regression estimators. Zbl 0465.62063
Trenkler, Götz
8
1980
Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052
Gnot, S.; Trenkler, G.; Zmyślony, R.
8
1995
Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005
Baksalary, Oskar Maria; Trenkler, Götz
8
2011
Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
8
2001
On generalized quadratic matrices. Zbl 1086.15504
Farebrother, Richard W.; Trenkler, Götz
7
2005
Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005
Wei, L.; Trenkler, G.
7
1995
Mean square error matrix comparisons among restricted least squares estimators. Zbl 0639.62060
Trenkler, Götz
7
1987
Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063
Stemann, D.; Trenkler, G.
7
1993
On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). Zbl 1222.15003
Baksalary, Oskar Maria; Trenkler, Götz
7
2011
On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631
Groß, J.; Trenkler, G.
7
1998
On a subspace metric based on matrix rank. Zbl 1202.15026
Baksalary, Oskar Maria; Trenkler, Götz
6
2010
Mean square error matrix superiority of estimators under linear restrictions and misspecification. Zbl 1328.62452
Wijekoon, P.; Trenkler, G.
6
1989
Between OLSE and BLUE. Zbl 1334.62106
Baksalary, Oskar Maria; Trenkler, Götz
6
2011
The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032
Trenkler, G.; Wei, L.
6
1996
Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060
Stahlecker, P.; Trenkler, G.
5
1991
Nichtparametrische statistische Methoden. Zbl 0369.62042
Büning, Herbert; Trenkler, Götz
5
1978
A multivariate version of Samuelson’s inequality. Zbl 1123.62048
Trenkler, Götz; Puntanen, Simo
5
2005
Third and fourth moment matrices of vec \(X'\) in multivariate analysis. Zbl 1009.62045
Neudecker, Heinz; Trenkler, Götz
5
2002
The vector cross product in \(\mathbb{C}^3\). Zbl 1018.15027
Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
5
1999
Further inequalities involving the Khatri-Rao product. Zbl 1179.15022
Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz
4
2009
Some remarks on a ridge-type-estimator and good prior means. Zbl 0696.62292
Trenkler, Götz
4
1988
On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006
Baksalary, Oskar Maria; Trenkler, Götz
4
2013
Minimax estimation with additional linear restrictions. A simulation study. Zbl 0695.62158
Schipp, B.; Trenkler, G.; Stahlecker, P.
4
1988
Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035
Trenkler, G.; Stahlecker, P.
4
1996
Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571
Toutenberg, H.; Trenkler, G.
4
1990
Records tests for trend in location. Zbl 0897.62044
Diersen, J.; Trenkler, G.
4
1996
Estimation from transformed data under the linear regression model. Zbl 0885.62080
Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen
4
1997
The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005
Schmidt, Karsten; Trenkler, Götz
4
2001
The vector cross product from an algebraic point of view. Zbl 0999.15033
Trenkler, Götz
3
2001
An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017
Baksalary, Oskar Maria; Trenkler, Götz
3
2008
On the product of rotations. Zbl 1474.97022
Trenkler, G.; Trenkler, D.
3
2008
A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062
Trenkler, Götz
3
1993
Let us do the twist again. Zbl 1416.62386
Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki
3
2013
Covariance adjustment in biased estimation. Zbl 0870.62042
Baksalary, Jerzy K.; Trenkler, Götz
3
1991
A simulation study comparing some biased estimators in the linear model. Zbl 0612.62096
Trenkler, D.; Trenkler, G.
3
1984
Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059
Neudecker, Heinz; Trenkler, Götz
3
2005
Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047
Groß, Jürgen; Trenkler, Götz; Liski, Erkki P.
3
1998
Nonlinear unbiased estimation in linear models. Zbl 0809.62057
Gnot, S.; Knautz, H.; Trenkler, G.; Zmyslony, R.
2
1992
Subsets and subspaces. Zbl 1188.15002
Baksalary, Oskar Maria; Trenkler, Götz
2
2010
A note on the correlation between \(S^ 2\) and the least squares estimator in the linear regression model. Zbl 0774.62070
Knautz, H.; Trenkler, G.
2
1993
Mean square error matrix superiority of the mixed regression estimator under misspecification. Zbl 0718.62153
Trenkler, Götz; Wijekoon, Pushba
2
1989
On a pair of vector spaces. Zbl 1292.15002
Baksalary, Oskar Maria; Trenkler, Götz
2
2013
Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059
Stahlecker, Peter; Knautz, Henning; Trenkler, Götz
2
1996
Singular magic squares. Zbl 0827.15003
Trenkler, Götz
2
1994
When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070
Groß, Jürgen; Trenkler, Götz
2
1997
On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix. Zbl 1510.15003
Baksalary, Oskar Maria; Trenkler, Götz
2
2021
Minimum mean square error ridge estimation. Zbl 0569.62059
Trenkler, Dietrich; Trenkler, Götz
2
1984
Vector equations and their solutions. Zbl 1025.15002
Trenkler, Götz
2
1998
On the entries of orthogonal projection matrices. Zbl 1266.15048
Baksalary, Oskar Maria; Trenkler, Götz
2
2013
On the Moore-Penrose inverse of a sum of matrices. Zbl 1518.15002
Baksalary, Oskar Maria; Sivakumar, K. C.; Trenkler, Götz
2
2023
On the correlation between \(\overline X\) and \(S^ 2\). Zbl 0784.62047
Knautz, Henning; Trenkler, Götz
1
1993
Mean square error matrix comparisons between biased restricted least squares estimators. Zbl 0746.62065
Trenkler, Götz
1
1991
Ein Vergleich des Kleinst-Quadrate-Schätzers mit verzerrten Alternativen. Zbl 0477.62050
Trenkler, Dietrich; Trenkler, Götz
1
1981
Problem 4/SP06: Estimation of the Hadamard and cross products of two mean vectors in multivariate analysis. Zbl 1125.62322
Neudecker, Heinz; Trenkler, Götz
1
2006
Introduction to modern matrix algebra. With applications to statistics. 2nd completely revised ed. (Einführung in die moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 1092.15001
Schmidt, Karsten; Trenkler, Götz
1
2006
Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060
Pordzik, Pawel R.; Trenkler, Götz
1
1994
Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056
Gnot, Stanisław; Knautz, Henning; Trenkler, Götz
1
1994
Introduction to modern matrix algebra. With applications to statistics. 3rd revised edition. (Einführung in die moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 1329.15003
Schmidt, Karsten; Trenkler, Götz
1
2015
A simple metric for finite dimensional vector spaces. Zbl 1313.15002
Baksalary, Oskar Maria; Trenkler, Götz
1
2012
On the equality of usual and Amemiya’s partially generalized least squares estimator. Zbl 0954.62547
Groß, Jürgen; Trenkler, Götz
1
1997
Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003
Trenkler, Götz
1
2004
Multivariate data, the arithmetic mean and exchangeability of transformations. Zbl 1080.62033
Frauendorf, Eckehard; Neudecker, Heinz; Trenkler, Götz
1
2005
On subspace distances determined by the Frobenius norm. Zbl 1286.15027
Baksalary, Oskar Maria; Trenkler, Götz
1
2014
On the Moore-Penrose inverse of a sum of matrices. Zbl 1518.15002
Baksalary, Oskar Maria; Sivakumar, K. C.; Trenkler, Götz
2
2023
On matrices whose Moore-Penrose inverse is idempotent. Zbl 1493.15009
Baksalary, Oskar Maria; Trenkler, Götz
1
2022
An alternative look at the linear regression model. Zbl 07612350
Baksalary, Oskar Maria; Trenkler, Götz
1
2022
On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix. Zbl 1510.15003
Baksalary, Oskar Maria; Trenkler, Götz
2
2021
A partial ordering approach to characterize properties of a pair of orthogonal projectors. Zbl 1477.15003
Baksalary, Oskar Maria; Trenkler, Götz
1
2021
Introduction to modern matrix algebra. With applications to statistics. 3rd revised edition. (Einführung in die moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 1329.15003
Schmidt, Karsten; Trenkler, Götz
1
2015
On a generalized core inverse. Zbl 1334.15009
Baksalary, Oskar Maria; Trenkler, Götz
57
2014
On subspace distances determined by the Frobenius norm. Zbl 1286.15027
Baksalary, Oskar Maria; Trenkler, Götz
1
2014
On \(k\)-potent matrices. Zbl 1283.15043
Baksalary, Oskar Maria; Trenkler, Götz
10
2013
On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006
Baksalary, Oskar Maria; Trenkler, Götz
4
2013
Let us do the twist again. Zbl 1416.62386
Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki
3
2013
On a pair of vector spaces. Zbl 1292.15002
Baksalary, Oskar Maria; Trenkler, Götz
2
2013
On the entries of orthogonal projection matrices. Zbl 1266.15048
Baksalary, Oskar Maria; Trenkler, Götz
2
2013
A simple metric for finite dimensional vector spaces. Zbl 1313.15002
Baksalary, Oskar Maria; Trenkler, Götz
1
2012
On disjoint range matrices. Zbl 1221.15005
Baksalary, Oskar Maria; Trenkler, Götz
13
2011
Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005
Baksalary, Oskar Maria; Trenkler, Götz
8
2011
On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). Zbl 1222.15003
Baksalary, Oskar Maria; Trenkler, Götz
7
2011
Between OLSE and BLUE. Zbl 1334.62106
Baksalary, Oskar Maria; Trenkler, Götz
6
2011
Core inverse of matrices. Zbl 1202.15009
Baksalary, Oskar Maria; Trenkler, Götz
253
2010
Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004
Baksalary, Oskar Maria; Trenkler, Götz
10
2010
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
10
2010
On a subspace metric based on matrix rank. Zbl 1202.15026
Baksalary, Oskar Maria; Trenkler, Götz
6
2010
Subsets and subspaces. Zbl 1188.15002
Baksalary, Oskar Maria; Trenkler, Götz
2
2010
Eigenspaces of the proper rotation matrices. Zbl 1292.97033
Baksalary, Oskar Maria; Trenkler, Götz
1
2010
On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004
Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz
33
2009
Revisitation of the product of two orthogonal projectors. Zbl 1167.15018
Baksalary, Oskar Maria; Trenkler, Götz
16
2009
Column space equalities for orthogonal projectors. Zbl 1169.15007
Baksalary, Oskar Maria; Trenkler, Götz
15
2009
A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165
Baksalary, Oskar Maria; Trenkler, Götz
11
2009
On angles and distances between subspaces. Zbl 1177.15024
Baksalary, Oskar Maria; Trenkler, Götz
11
2009
Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010
Baksalary, Oskar Maria; Trenkler, Götz
9
2009
Further inequalities involving the Khatri-Rao product. Zbl 1179.15022
Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz
4
2009
Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008
Liu, Shuangzhe; Trenkler, Götz
44
2008
Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023
Baksalary, Oskar Maria; Trenkler, Götz
28
2008
Further results on generalized and hypergeneralized projectors. Zbl 1151.15022
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz
17
2008
An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017
Baksalary, Oskar Maria; Trenkler, Götz
3
2008
On the product of rotations. Zbl 1474.97022
Trenkler, G.; Trenkler, D.
3
2008
Problem 4/SP06: Estimation of the Hadamard and cross products of two mean vectors in multivariate analysis. Zbl 1125.62322
Neudecker, Heinz; Trenkler, Götz
1
2006
Introduction to modern matrix algebra. With applications to statistics. 2nd completely revised ed. (Einführung in die moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 1092.15001
Schmidt, Karsten; Trenkler, Götz
1
2006
On generalized quadratic matrices. Zbl 1086.15504
Farebrother, Richard W.; Trenkler, Götz
7
2005
A multivariate version of Samuelson’s inequality. Zbl 1123.62048
Trenkler, Götz; Puntanen, Simo
5
2005
Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059
Neudecker, Heinz; Trenkler, Götz
3
2005
Multivariate data, the arithmetic mean and exchangeability of transformations. Zbl 1080.62033
Frauendorf, Eckehard; Neudecker, Heinz; Trenkler, Götz
1
2005
The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Zbl 1164.15317
Trenkler, G.; Trenkler, D.
1
2005
Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003
Trenkler, Götz
1
2004
A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz
11
2003
Third and fourth moment matrices of vec \(X'\) in multivariate analysis. Zbl 1009.62045
Neudecker, Heinz; Trenkler, Götz
5
2002
Maximum likelihood estimation in mixed normal models with two variance components. Zbl 1003.62017
Gnot, S.; Stemann, D.; Trenkler, G.; Urbańska-Motyka, A.
1
2002
The Moore-Penrose inverse and the vector product. Zbl 1012.15004
Trenkler, Götz
1
2002
The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056
Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim
11
2001
Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
8
2001
The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005
Schmidt, Karsten; Trenkler, Götz
4
2001
The vector cross product from an algebraic point of view. Zbl 0999.15033
Trenkler, Götz
3
2001
On the efficiency of the Cochrane-Orcutt estimator in the serially correlated error components regression model for panel data. Zbl 1009.62555
Song, Seuck Heun; Trenkler, Götz
1
2001
Some further results on the efficiency of the Cochrane-Orcutt-estimator. Zbl 0951.62057
Stemann, D.; Trenkler, G.
1
2000
Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020
Gross, Jürgen; Trenkler, Götz
34
1999
On semi-orthogonality and a special class of matrices. Zbl 0949.15036
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
10
1999
The vector cross product in \(\mathbb{C}^3\). Zbl 1018.15027
Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
5
1999
On the eigenvalues of \(3\times 3\) magic squares. Zbl 1017.05029
Trenkler, Götz
1
1999
On properties of \(3\times 3\) semi-magic squares. Zbl 1017.05028
Gross, J.; Troschke, S.-O.; Trenkler, G.
1
1999
On the product of oblique projectors. Zbl 0929.15016
Groß, Jürgen; Trenkler, Götz
12
1998
On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631
Groß, J.; Trenkler, G.
7
1998
Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047
Groß, Jürgen; Trenkler, Götz; Liski, Erkki P.
3
1998
Vector equations and their solutions. Zbl 1025.15002
Trenkler, Götz
2
1998
Modern matrix algebra. With applications to statistics. (Moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 0897.15002
Schmidt, Karsten; Trenkler, Götz
1
1998
Using first differences as a device against multicollinearity. Zbl 0936.91054
Toutenburg, Helge; Trenkler, Götz
1
1998
Generalized and hypergeneralized projectors. Zbl 0887.15024
Groß, Jürgen; Trenkler, Götz
32
1997
Estimation from transformed data under the linear regression model. Zbl 0885.62080
Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen
4
1997
When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070
Groß, Jürgen; Trenkler, Götz
2
1997
On the equality of usual and Amemiya’s partially generalized least squares estimator. Zbl 0954.62547
Groß, Jürgen; Trenkler, Götz
1
1997
The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032
Trenkler, G.; Wei, L.
6
1996
Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035
Trenkler, G.; Stahlecker, P.
4
1996
Records tests for trend in location. Zbl 0897.62044
Diersen, J.; Trenkler, G.
4
1996
Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059
Stahlecker, Peter; Knautz, Henning; Trenkler, Götz
2
1996
On the least squares distance between affine subspaces. Zbl 0852.15003
Gross, Jürgen; Trenkler, Götz
1
1996
Nonnegative quadratic estimation of the mean squared errors of minimax estimators in the linear regression model. Zbl 0844.62053
Gnot, S.; Trenkler, G.
1
1996
Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052
Gnot, S.; Trenkler, G.; Zmyślony, R.
8
1995
Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005
Wei, L.; Trenkler, G.
7
1995
Some bounds for bias and variance of \(S^ 2\) under dependence. Zbl 0819.62019
Knautz, Henning; Trenkler, Götz
1
1995
An objective stability criterion for selecting the biasing parameter from the ridge trace. Zbl 0861.62056
Trenkler, Dietrich; Trenkler, Götz
1
1995
Characterizations of oblique and orthogonal projectors. Zbl 0827.62054
Trenkler, Götz
11
1994
Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. (Nichtparametrische statistische Methoden.) Zbl 0820.62031
Büning, Herbert; Trenkler, Götz
8
1994
Singular magic squares. Zbl 0827.15003
Trenkler, Götz
2
1994
Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060
Pordzik, Pawel R.; Trenkler, Götz
1
1994
Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056
Gnot, Stanisław; Knautz, Henning; Trenkler, Götz
1
1994
Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061
Stahlecker, Peter; Trenkler, Götz
10
1993
Minimum mean square error estimation in linear regression. Zbl 0786.62068
Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz
9
1993
Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063
Stemann, D.; Trenkler, G.
7
1993
A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062
Trenkler, Götz
3
1993
A note on the correlation between \(S^ 2\) and the least squares estimator in the linear regression model. Zbl 0774.62070
Knautz, H.; Trenkler, G.
2
1993
On the correlation between \(\overline X\) and \(S^ 2\). Zbl 0784.62047
Knautz, Henning; Trenkler, Götz
1
1993
Some further results on Hermitian-matrix inequalities. Zbl 0753.15014
Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz
15
1992
Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093
Trenkler, G.; Toutenburg, H.
8
1992
Nonlinear unbiased estimation in linear models. Zbl 0809.62057
Gnot, S.; Knautz, H.; Trenkler, G.; Zmyslony, R.
2
1992
Pre-test estimation in the linear regression model with competing linear constraints. Zbl 0770.62052
Hessenius, Helga; Trenkler, Götz
1
1992
Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011
Baksalary, Jerzy K.; Trenkler, Götz
29
1991
Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060
Stahlecker, P.; Trenkler, G.
5
1991
Covariance adjustment in biased estimation. Zbl 0870.62042
Baksalary, Jerzy K.; Trenkler, Götz
3
1991
Mean square error matrix comparisons between biased restricted least squares estimators. Zbl 0746.62065
Trenkler, Götz
1
1991
Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066
Trenkler, G.; Toutenburg, H.
72
1990
Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571
Toutenberg, H.; Trenkler, G.
4
1990
...and 20 more Documents
all top 5

Cited by 682 Authors

72 Trenkler, Götz
65 Mosić, Dijana
58 Chen, Jianlong
40 Baksalary, Oskar Maria
31 Thome, Néstor
27 Stanimirović, Predrag S.
23 Benítez Lopez, Julio
23 Liu, Xiaoji
23 Stahlecker, Peter
20 Tian, Yongge
18 Gross, Jürgen
18 Xu, Sanzhang
17 Ma, Haifeng
17 Özkale, M. Revan
17 Yang, Hu
16 Deng, Chunyuan
15 Ferreyra, David Eduardo
14 Baksalary, Jerzy K.
14 Wang, Hongxing
13 Kaçıranlar, Selahattin
13 Kyrchei, Ivan I.
13 Li, Tingting
13 Zhou, Mengmeng
12 Đorđević, Dragan S.
12 Puntanen, Simo
12 Zhu, Huihui
12 Zuo, Kezheng
11 Gao, Yuefeng
11 Malik, Saroj B.
11 Wei, Laisheng
11 Wei, Yimin
10 Liski, Erkki P.
9 Cvetković-Ilić, Dragana S.
9 Kibria, B. M. Golam
9 Özdemir, Halim
9 Patrício, Pedro
8 Markiewicz, Augustyn
8 Ohtani, Kazuhiro
8 Toutenburg, Helge
8 Wu, Jibo
7 Akdeniz, Fikri
7 Behera, Ratikanta
7 Dawoud, Issam
7 Liu, Shuangzhe
7 Rakočević, Vladimir
7 Sahoo, Jajati Keshari
7 Wang, Dingguo
7 Wijekoon, Pushpakanthie
7 Zhou, Yukun
6 Arnold, Bernhard F.
6 Chen, Xiaofeng
6 Levis, Fabián Eduardo
6 Li, Yalian
6 Marovt, Janko
6 Rakić, Dragan S.
6 Schipp, Bernhard
6 Styan, George P. H.
5 Açar, Tuğba Söküt
5 Akram, Muhammad Nauman
5 Amin, Muhammad Shoib
5 Aslam, Muhammad
5 Koliha, Jerry J.
5 Lebtahi, Leila
5 Matvejchuk, Marjan Stepanovich
5 Özbay, Nimet
5 Schmidt, Karsten
5 Wang, Long
5 Wei, Junchao
5 Zhang, Daochang
5 Zou, Honglin
4 Arumairajan, Sivarajah
4 Corach, Gustavo
4 Dinčić, Nebojša Č.
4 Germider, Oksana Vladimirovna
4 Hauke, Jan
4 Hurley, Ted
4 Ke, Yuanyuan
4 Kuran, Özge
4 Lattanzi, Marina Beatriz
4 Lukman, Adewale F.
4 Popov, Vasily Nikolaevich
4 Radicic, Biljana M.
4 Roozbeh, Mahdi
4 Sakallioglu, Sadullah
4 Sivakumar, Koratti Chengalrayan
4 Trenkler, Dietrich
4 Wang, Lichun
4 Wang, Qingwen
4 Wu, Cang
4 Zhang, WeiPing
3 Abonazel, Mohamed Reda
3 Ahmed, Syed Ejaz
3 Beites, Patrícia Damas
3 Büning, Herbert
3 Catral, Minerva
3 Chandra, Shalini
3 Chang, Xinfeng
3 Djikić, Marko S.
3 Dolinar, Gregor
3 Du, Hongke
...and 582 more Authors
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Cited in 166 Serials

91 Linear Algebra and its Applications
90 Linear and Multilinear Algebra
61 Communications in Statistics. Theory and Methods
53 Statistical Papers
36 Applied Mathematics and Computation
33 Communications in Statistics. Simulation and Computation
27 Journal of Statistical Planning and Inference
22 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
17 Filomat
15 Journal of Statistical Computation and Simulation
13 Statistics & Probability Letters
12 Acta Applicandae Mathematicae
12 Statistics
9 Communications in Algebra
9 Quaestiones Mathematicae
9 Computational and Applied Mathematics
9 Journal of Algebra and its Applications
9 Open Mathematics
8 Journal of Multivariate Analysis
8 Aequationes Mathematicae
8 Advances in Applied Clifford Algebras
7 International Journal of Mathematical Education in Science and Technology
7 ELA. The Electronic Journal of Linear Algebra
7 Journal of Applied Statistics
7 Frontiers of Mathematics in China
6 Journal of Mathematical Analysis and Applications
6 Journal of Computational and Applied Mathematics
6 Computational Statistics and Data Analysis
6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
6 Mediterranean Journal of Mathematics
6 Special Matrices
5 Indian Journal of Pure & Applied Mathematics
5 Journal of Mathematics
4 Computers & Mathematics with Applications
4 Metrika
4 Journal of Econometrics
4 Results in Mathematics
4 Bulletin of the Iranian Mathematical Society
4 Statistische Hefte
4 Numerical Linear Algebra with Applications
4 Turkish Journal of Mathematics
4 Hacettepe Journal of Mathematics and Statistics
4 Banach Journal of Mathematical Analysis
3 Automatica
3 Acta Mathematicae Applicatae Sinica. English Series
3 Computational Statistics
3 Test
3 Lobachevskii Journal of Mathematics
3 Journal of Applied Mathematics and Computing
3 Statistical Methods and Applications
2 The American Statistician
2 International Journal of Theoretical Physics
2 Psychometrika
2 Rocky Mountain Journal of Mathematics
2 Ukrainian Mathematical Journal
2 Biometrical Journal
2 Czechoslovak Mathematical Journal
2 Numerical Functional Analysis and Optimization
2 Statistica Neerlandica
2 Bulletin of the Korean Mathematical Society
2 Applied Mathematics Letters
2 Mathematical and Computer Modelling
2 SIAM Journal on Matrix Analysis and Applications
2 Economics Letters
2 Computational Mathematics and Mathematical Physics
2 Wuhan University Journal of Natural Sciences (WUJNS)
2 Thailand Statistician
2 Advances and Applications in Discrete Mathematics
2 International Journal of Group Theory
2 Communications in Mathematics and Statistics
2 Journal of Linear and Topological Algebra
2 AIMS Mathematics
1 American Mathematical Monthly
1 Discrete Mathematics
1 Fluid Dynamics
1 Inverse Problems
1 Journal of Computational Physics
1 Journal of the Franklin Institute
1 Journal of Mathematical Physics
1 Mathematical Methods in the Applied Sciences
1 Scandinavian Journal of Statistics
1 Chaos, Solitons and Fractals
1 Beiträge zur Algebra und Geometrie
1 Acta Scientiarum Mathematicarum
1 Annals of the Institute of Statistical Mathematics
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 The Annals of Statistics
1 Biometrics
1 BIT
1 Calcolo
1 Collectanea Mathematica
1 Econometrica
1 Information Sciences
1 International Journal of Mathematics and Mathematical Sciences
1 International Statistical Review
1 Journal of Algebra
1 Journal of the Korean Mathematical Society
1 Journal of Pure and Applied Algebra
1 Mathematica Slovaca
1 Proceedings of the American Mathematical Society
...and 66 more Serials
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Cited in 44 Fields

400 Linear and multilinear algebra; matrix theory (15-XX)
338 Statistics (62-XX)
89 Associative rings and algebras (16-XX)
86 Operator theory (47-XX)
68 Numerical analysis (65-XX)
33 Functional analysis (46-XX)
31 Order, lattices, ordered algebraic structures (06-XX)
15 Computer science (68-XX)
8 Number theory (11-XX)
8 Operations research, mathematical programming (90-XX)
7 Group theory and generalizations (20-XX)
7 Probability theory and stochastic processes (60-XX)
7 Quantum theory (81-XX)
7 Systems theory; control (93-XX)
5 Combinatorics (05-XX)
5 Category theory; homological algebra (18-XX)
5 Geometry (51-XX)
5 Information and communication theory, circuits (94-XX)
4 Mathematical logic and foundations (03-XX)
4 Algebraic geometry (14-XX)
4 Ordinary differential equations (34-XX)
4 Mathematics education (97-XX)
3 Partial differential equations (35-XX)
3 Fluid mechanics (76-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 General algebraic systems (08-XX)
2 Nonassociative rings and algebras (17-XX)
2 Difference and functional equations (39-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Real functions (26-XX)
1 Measure and integration (28-XX)
1 Functions of a complex variable (30-XX)
1 Special functions (33-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Approximations and expansions (41-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Integral transforms, operational calculus (44-XX)
1 Differential geometry (53-XX)
1 Mechanics of deformable solids (74-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Biology and other natural sciences (92-XX)

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