Edit Profile (opens in new tab) Trenkler, Götz Co-Author Distance Author ID: trenkler.gotz 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 Co-Authors 21 single-authored 38 Baksalary, Oskar Maria 17 Trenkler, Dietrich 15 Gross, Jürgen 11 Stahlecker, Peter 9 Knautz, Henning 7 Gnot, Stanisław 7 Liski, Erkki P. 6 Baksalary, Jerzy K. 6 Schmidt, Karsten 5 Stemann, Dietmar 5 Toutenburg, Helge 5 Troschke, Sven-Oliver 4 Ihorst, Gabriele 4 Neudecker, Heinz 4 Schipp, Bernhard 4 Wei, Laisheng 3 Liu, Shuangzhe 3 Styan, George P. H. 2 Büning, Herbert 2 Pordzik, Paweł R. 2 Urbańska-Motyka, Agnieszka 2 Wijekoon, Pushba 2 Zmyślony, Roman 1 Ahmed, Syed Ejaz 1 Bernstein, Dennis S. 1 Diersen, J. 1 Farebrother, Richard William 1 Frauendorf, Eckehard 1 Freund, Eckhard 1 Hering, Franz 1 Hessenius, Helga 1 Heun Song, Seuck 1 Hunter, Jeffrey J. 1 Kollo, Tõnu 1 Liu, Xiaoji 1 Markiewicz, Augustyn 1 Michels, Paul 1 Puntanen, Simo 1 Ruiz Espejo, Mariano 1 Saxena, Sharad 1 Schach, Siegfried 1 Singh, Housila Prasad 1 Sivakumar, Koratti Chengalrayan 1 Tamaschke, Sabine 1 Toutenberg, H. 1 von Rosen, Dietrich 1 Werner, Hans-Joachim 1 Yang, Zhongpeng 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 all top 5 Fields 100 Statistics (62-XX) 70 Linear and multilinear algebra; matrix theory (15-XX) 7 Combinatorics (05-XX) 6 Mathematics education (97-XX) 4 General and overarching topics; collections (00-XX) 3 Geometry (51-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 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. 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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 all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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