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: 159 Publications since 1976, including 6 Books 3 Contributions as Editor Biographic References: 1 Publication Co-Authors: 46 Co-Authors with 141 Joint Publications 774 Co-Co-Authors all top 5 Co-Authors 21 single-authored 37 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 Styan, George P. H. 2 Büning, Herbert 2 Liu, Shuangzhe 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 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 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 7 Applied Mathematics and Computation 7 Journal of Statistical Planning and Inference 7 Statistical Papers 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 all top 5 Fields 99 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 113 Publications have been cited 1,076 times in 752 Documents Cited by ▼ Year ▼ Core inverse of matrices. Zbl 1202.15009Baksalary, Oskar Maria; Trenkler, Götz 214 2010 Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066Trenkler, G.; Toutenburg, H. 67 1990 On a generalized core inverse. Zbl 1334.15009Baksalary, Oskar Maria; Trenkler, Götz 44 2014 Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020Gross, Jürgen; Trenkler, Götz 33 1999 Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008Liu, Shuangzhe; Trenkler, Götz 31 2008 On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. Zbl 0559.62054Trenkler, Götz 31 1984 On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz 31 2009 Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011Baksalary, Jerzy K.; Trenkler, Götz 29 1991 Generalized and hypergeneralized projectors. Zbl 0887.15024Groß, Jürgen; Trenkler, Götz 29 1997 Quasi minimax-estimation in the linear regression model. Zbl 0635.62066Trenkler, G.; Stahlecker, P. 28 1987 Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023Baksalary, Oskar Maria; Trenkler, Götz 26 2008 Mean square error matrix comparisons of estimators in linear regression. Zbl 0594.62075Trenkler, Götz 19 1985 Further results on generalized and hypergeneralized projectors. Zbl 1151.15022Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz 17 2008 Mean square error matrix improvements and admissibility of linear estimators. Zbl 0685.62052Baksalary, Jerzy K.; Liski, Erkki P.; Trenkler, Götz 16 1989 Revisitation of the product of two orthogonal projectors. Zbl 1167.15018Baksalary, Oskar Maria; Trenkler, Götz 16 2009 Column space equalities for orthogonal projectors. Zbl 1169.15007Baksalary, Oskar Maria; Trenkler, Götz 15 2009 Some further results on Hermitian-matrix inequalities. Zbl 0753.15014Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz 14 1992 Biased estimators in the linear regression model. Zbl 0471.62070Trenkler, Götz 13 1981 On disjoint range matrices. Zbl 1221.15005Baksalary, Oskar Maria; Trenkler, Götz 13 2011 On the product of oblique projectors. Zbl 0929.15016Groß, Jürgen; Trenkler, Götz 12 1998 A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165Baksalary, Oskar Maria; Trenkler, Götz 11 2009 A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz 11 2003 Characterizations of oblique and orthogonal projectors. Zbl 0827.62054Trenkler, Götz 11 1994 The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim 11 2001 On angles and distances between subspaces. Zbl 1177.15024Baksalary, Oskar Maria; Trenkler, Götz 11 2009 Full and partial minimax estimation in regression analysis with additional linear constraints. Zbl 0653.62053Stahlecker, P.; Trenkler, G. 10 1988 Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061Stahlecker, Peter; Trenkler, Götz 10 1993 A note on superiority comparisons of homogeneous linear estimators. Zbl 0523.62066Trenkler, Götz; Trenkler, Dietrich 10 1983 On semi-orthogonality and a special class of matrices. Zbl 0949.15036Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 10 1999 Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004Baksalary, Oskar Maria; Trenkler, Götz 10 2010 Partial minimax estimation in regression analysis. Zbl 0647.62063Hering, F.; Trenkler, G.; Stahlecker, P. 9 1987 Minimum mean square error estimation in linear regression. Zbl 0786.62068Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz 9 1993 Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010Baksalary, Oskar Maria; Trenkler, Götz 9 2009 Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005Baksalary, Oskar Maria; Trenkler, Götz 8 2011 Generalized mean squared error comparisons of biased regression estimators. Zbl 0465.62063Trenkler, Götz 8 1980 Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052Gnot, S.; Trenkler, G.; Zmyślony, R. 8 1995 On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz 8 2010 Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093Trenkler, G.; Toutenburg, H. 7 1992 Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063Stemann, D.; Trenkler, G. 7 1993 Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 7 2001 Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005Wei, L.; Trenkler, G. 7 1995 On \(k\)-potent matrices. Zbl 1283.15043Baksalary, Oskar Maria; Trenkler, Götz 7 2013 Mean square error matrix comparisons among restricted least squares estimators. Zbl 0639.62060Trenkler, Götz 6 1987 Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. (Nichtparametrische statistische Methoden.) Zbl 0820.62031Büning, Herbert; Trenkler, Götz 6 1994 On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631Groß, J.; Trenkler, G. 6 1998 On a subspace metric based on matrix rank. Zbl 1202.15026Baksalary, Oskar Maria; Trenkler, Götz 6 2010 On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). Zbl 1222.15003Baksalary, Oskar Maria; Trenkler, Götz 6 2011 On generalized quadratic matrices. Zbl 1086.15504Farebrother, Richard W.; Trenkler, Götz 5 2005 Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060Stahlecker, P.; Trenkler, G. 5 1991 Nichtparametrische statistische Methoden. Zbl 0369.62042Büning, Herbert; Trenkler, Götz 5 1978 The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032Trenkler, G.; Wei, L. 5 1996 Between OLSE and BLUE. Zbl 1334.62106Baksalary, Oskar Maria; Trenkler, Götz 5 2011 Estimation from transformed data under the linear regression model. Zbl 0885.62080Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen 4 1997 Minimax estimation with additional linear restrictions. A simulation study. Zbl 0695.62158Schipp, B.; Trenkler, G.; Stahlecker, P. 4 1988 Some remarks on a ridge-type-estimator and good prior means. Zbl 0696.62292Trenkler, Götz 4 1988 Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571Toutenberg, H.; Trenkler, G. 4 1990 The vector cross product in \(\mathbb{C}^3\). Zbl 1018.15027Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 4 1999 Third and fourth moment matrices of vec \(X'\) in multivariate analysis. Zbl 1009.62045Neudecker, Heinz; Trenkler, Götz 4 2002 Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035Trenkler, G.; Stahlecker, P. 4 1996 Records tests for trend in location. Zbl 0897.62044Diersen, J.; Trenkler, G. 4 1996 On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006Baksalary, Oskar Maria; Trenkler, Götz 4 2013 Mean square error matrix superiority of estimators under linear restrictions and misspecification. Zbl 1328.62452Wijekoon, P.; Trenkler, G. 4 1989 An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017Baksalary, Oskar Maria; Trenkler, Götz 3 2008 A multivariate version of Samuelson’s inequality. Zbl 1123.62048Trenkler, Götz; Puntanen, Simo 3 2005 A simulation study comparing some biased estimators in the linear model. Zbl 0612.62096Trenkler, D.; Trenkler, G. 3 1984 A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062Trenkler, Götz 3 1993 Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047Groß, Jürgen; Trenkler, Götz; Liski, Erkki P. 3 1998 The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005Schmidt, Karsten; Trenkler, Götz 3 2001 The vector cross product from an algebraic point of view. Zbl 0999.15033Trenkler, Götz 3 2001 Covariance adjustment in biased estimation. Zbl 0870.62042Baksalary, Jerzy K.; Trenkler, Götz 3 1991 On the product of rotations. Zbl 1474.97022Trenkler, G.; Trenkler, D. 3 2008 Let us do the twist again. Zbl 1416.62386Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki 3 2013 A note on the correlation between \(S^ 2\) and the least squares estimator in the linear regression model. Zbl 0774.62070Knautz, H.; Trenkler, G. 2 1993 Subsets and subspaces. Zbl 1188.15002Baksalary, Oskar Maria; Trenkler, Götz 2 2010 Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059Neudecker, Heinz; Trenkler, Götz 2 2005 Minimum mean square error ridge estimation. Zbl 0569.62059Trenkler, Dietrich; Trenkler, Götz 2 1984 Mean square error matrix superiority of the mixed regression estimator under misspecification. Zbl 0718.62153Trenkler, Götz; Wijekoon, Pushba 2 1989 Singular magic squares. Zbl 0827.15003Trenkler, Götz 2 1994 Vector equations and their solutions. Zbl 1025.15002Trenkler, Götz 2 1998 On the entries of orthogonal projection matrices. Zbl 1266.15048Baksalary, Oskar Maria; Trenkler, Götz 2 2013 Further inequalities involving the Khatri-Rao product. Zbl 1179.15022Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz 2 2009 Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059Stahlecker, Peter; Knautz, Henning; Trenkler, Götz 2 1996 When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070Groß, Jürgen; Trenkler, Götz 2 1997 On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix. Zbl 1510.15003Baksalary, Oskar Maria; Trenkler, Götz 2 2021 On a pair of vector spaces. Zbl 1292.15002Baksalary, Oskar Maria; Trenkler, Götz 2 2013 Mean square error matrix comparisons between mixed estimators. Zbl 0626.62052Freund, E.; Trenkler, G. 1 1986 Mean square error matrix comparisons between biased restricted least squares estimators. Zbl 0746.62065Trenkler, Götz 1 1991 On the correlation between \(\overline X\) and \(S^ 2\). Zbl 0784.62047Knautz, Henning; Trenkler, Götz 1 1993 Pre-test estimation in the linear regression model with competing linear constraints. Zbl 0770.62052Hessenius, Helga; Trenkler, Götz 1 1992 The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Zbl 1164.15317Trenkler, G.; Trenkler, D. 1 2005 Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003Trenkler, Götz 1 2004 On the Euclidean distance between biased estimators. Zbl 0565.62044Trenkler, Dietrich; Trenkler, Götz 1 1984 Ein Vergleich des Kleinst-Quadrate-Schätzers mit verzerrten Alternativen. Zbl 0477.62050Trenkler, Dietrich; Trenkler, Götz 1 1981 Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060Pordzik, Pawel R.; Trenkler, Götz 1 1994 Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056Gnot, Stanisław; Knautz, Henning; Trenkler, Götz 1 1994 Some bounds for bias and variance of \(S^ 2\) under dependence. Zbl 0819.62019Knautz, Henning; Trenkler, Götz 1 1995 Using first differences as a device against multicollinearity. Zbl 0936.91054Toutenburg, Helge; Trenkler, Götz 1 1998 On the eigenvalues of \(3\times 3\) magic squares. Zbl 1017.05029Trenkler, Götz 1 1999 On properties of \(3\times 3\) semi-magic squares. Zbl 1017.05028Gross, J.; Troschke, S.-O.; Trenkler, G. 1 1999 The Moore-Penrose inverse and the vector product. Zbl 1012.15004Trenkler, Götz 1 2002 On the Moore-Penrose inverse of a sum of matrices. Zbl 07683139Baksalary, Oskar Maria; Sivakumar, K. C.; Trenkler, Götz 1 2023 On matrices whose Moore-Penrose inverse is idempotent. Zbl 1493.15009Baksalary, Oskar Maria; Trenkler, Götz 1 2022 On formulae for the Moore-Penrose inverse of a columnwise partitioned matrix. Zbl 1510.15003Baksalary, Oskar Maria; Trenkler, Götz 2 2021 A partial ordering approach to characterize properties of a pair of orthogonal projectors. Zbl 1477.15003Baksalary, Oskar Maria; Trenkler, Götz 1 2021 On a generalized core inverse. Zbl 1334.15009Baksalary, Oskar Maria; Trenkler, Götz 44 2014 On subspace distances determined by the Frobenius norm. Zbl 1286.15027Baksalary, Oskar Maria; Trenkler, Götz 1 2014 On \(k\)-potent matrices. Zbl 1283.15043Baksalary, Oskar Maria; Trenkler, Götz 7 2013 On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006Baksalary, Oskar Maria; Trenkler, Götz 4 2013 Let us do the twist again. Zbl 1416.62386Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki 3 2013 On the entries of orthogonal projection matrices. Zbl 1266.15048Baksalary, Oskar Maria; Trenkler, Götz 2 2013 On a pair of vector spaces. Zbl 1292.15002Baksalary, Oskar Maria; Trenkler, Götz 2 2013 A simple metric for finite dimensional vector spaces. Zbl 1313.15002Baksalary, Oskar Maria; Trenkler, Götz 1 2012 On disjoint range matrices. Zbl 1221.15005Baksalary, Oskar Maria; Trenkler, Götz 13 2011 Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005Baksalary, Oskar Maria; Trenkler, Götz 8 2011 On the projectors \(\mathbf F\mathbf F^\dagger\) and \(\mathbf F^\dagger\mathbf F\). Zbl 1222.15003Baksalary, Oskar Maria; Trenkler, Götz 6 2011 Between OLSE and BLUE. Zbl 1334.62106Baksalary, Oskar Maria; Trenkler, Götz 5 2011 Core inverse of matrices. Zbl 1202.15009Baksalary, Oskar Maria; Trenkler, Götz 214 2010 Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004Baksalary, Oskar Maria; Trenkler, Götz 10 2010 On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz 8 2010 On a subspace metric based on matrix rank. Zbl 1202.15026Baksalary, Oskar Maria; Trenkler, Götz 6 2010 Subsets and subspaces. Zbl 1188.15002Baksalary, Oskar Maria; Trenkler, Götz 2 2010 Eigenspaces of the proper rotation matrices. Zbl 1292.97033Baksalary, Oskar Maria; Trenkler, Götz 1 2010 On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz 31 2009 Revisitation of the product of two orthogonal projectors. Zbl 1167.15018Baksalary, Oskar Maria; Trenkler, Götz 16 2009 Column space equalities for orthogonal projectors. Zbl 1169.15007Baksalary, Oskar Maria; Trenkler, Götz 15 2009 A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165Baksalary, Oskar Maria; Trenkler, Götz 11 2009 On angles and distances between subspaces. Zbl 1177.15024Baksalary, Oskar Maria; Trenkler, Götz 11 2009 Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010Baksalary, Oskar Maria; Trenkler, Götz 9 2009 Further inequalities involving the Khatri-Rao product. Zbl 1179.15022Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz 2 2009 Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008Liu, Shuangzhe; Trenkler, Götz 31 2008 Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023Baksalary, Oskar Maria; Trenkler, Götz 26 2008 Further results on generalized and hypergeneralized projectors. Zbl 1151.15022Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz 17 2008 An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017Baksalary, Oskar Maria; Trenkler, Götz 3 2008 On the product of rotations. Zbl 1474.97022Trenkler, G.; Trenkler, D. 3 2008 On generalized quadratic matrices. Zbl 1086.15504Farebrother, Richard W.; Trenkler, Götz 5 2005 A multivariate version of Samuelson’s inequality. Zbl 1123.62048Trenkler, Götz; Puntanen, Simo 3 2005 Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059Neudecker, Heinz; Trenkler, Götz 2 2005 The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Zbl 1164.15317Trenkler, G.; Trenkler, D. 1 2005 Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003Trenkler, Götz 1 2004 A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz 11 2003 Third and fourth moment matrices of vec \(X'\) in multivariate analysis. Zbl 1009.62045Neudecker, Heinz; Trenkler, Götz 4 2002 The Moore-Penrose inverse and the vector product. Zbl 1012.15004Trenkler, Götz 1 2002 The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim 11 2001 Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 7 2001 The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005Schmidt, Karsten; Trenkler, Götz 3 2001 The vector cross product from an algebraic point of view. Zbl 0999.15033Trenkler, Götz 3 2001 On the efficiency of the Cochrane-Orcutt estimator in the serially correlated error components regression model for panel data. Zbl 1009.62555Song, Seuck Heun; Trenkler, Götz 1 2001 Some further results on the efficiency of the Cochrane-Orcutt-estimator. Zbl 0951.62057Stemann, D.; Trenkler, G. 1 2000 Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020Gross, Jürgen; Trenkler, Götz 33 1999 On semi-orthogonality and a special class of matrices. Zbl 0949.15036Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 10 1999 The vector cross product in \(\mathbb{C}^3\). Zbl 1018.15027Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver 4 1999 On the eigenvalues of \(3\times 3\) magic squares. Zbl 1017.05029Trenkler, Götz 1 1999 On properties of \(3\times 3\) semi-magic squares. Zbl 1017.05028Gross, J.; Troschke, S.-O.; Trenkler, G. 1 1999 On the product of oblique projectors. Zbl 0929.15016Groß, Jürgen; Trenkler, Götz 12 1998 On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631Groß, J.; Trenkler, G. 6 1998 Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047Groß, Jürgen; Trenkler, Götz; Liski, Erkki P. 3 1998 Vector equations and their solutions. Zbl 1025.15002Trenkler, Götz 2 1998 Using first differences as a device against multicollinearity. Zbl 0936.91054Toutenburg, Helge; Trenkler, Götz 1 1998 Modern matrix algebra. With applications to statistics. (Moderne Matrix-Algebra. Mit Anwendungen in der Statistik.) Zbl 0897.15002Schmidt, Karsten; Trenkler, Götz 1 1998 Generalized and hypergeneralized projectors. Zbl 0887.15024Groß, Jürgen; Trenkler, Götz 29 1997 Estimation from transformed data under the linear regression model. Zbl 0885.62080Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen 4 1997 When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070Groß, Jürgen; Trenkler, Götz 2 1997 On the equality of usual and Amemiya’s partially generalized least squares estimator. Zbl 0954.62547Groß, Jürgen; Trenkler, Götz 1 1997 The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032Trenkler, G.; Wei, L. 5 1996 Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035Trenkler, G.; Stahlecker, P. 4 1996 Records tests for trend in location. Zbl 0897.62044Diersen, J.; Trenkler, G. 4 1996 Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059Stahlecker, Peter; Knautz, Henning; Trenkler, Götz 2 1996 On the least squares distance between affine subspaces. Zbl 0852.15003Gross, Jürgen; Trenkler, Götz 1 1996 Nonnegative quadratic estimation of the mean squared errors of minimax estimators in the linear regression model. Zbl 0844.62053Gnot, S.; Trenkler, G. 1 1996 Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052Gnot, S.; Trenkler, G.; Zmyślony, R. 8 1995 Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005Wei, L.; Trenkler, G. 7 1995 Some bounds for bias and variance of \(S^ 2\) under dependence. Zbl 0819.62019Knautz, Henning; Trenkler, Götz 1 1995 An objective stability criterion for selecting the biasing parameter from the ridge trace. Zbl 0861.62056Trenkler, Dietrich; Trenkler, Götz 1 1995 Characterizations of oblique and orthogonal projectors. Zbl 0827.62054Trenkler, Götz 11 1994 Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. (Nichtparametrische statistische Methoden.) Zbl 0820.62031Büning, Herbert; Trenkler, Götz 6 1994 Singular magic squares. Zbl 0827.15003Trenkler, Götz 2 1994 Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060Pordzik, Pawel R.; Trenkler, Götz 1 1994 Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056Gnot, Stanisław; Knautz, Henning; Trenkler, Götz 1 1994 Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061Stahlecker, Peter; Trenkler, Götz 10 1993 Minimum mean square error estimation in linear regression. Zbl 0786.62068Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz 9 1993 Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063Stemann, D.; Trenkler, G. 7 1993 A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062Trenkler, Götz 3 1993 A note on the correlation between \(S^ 2\) and the least squares estimator in the linear regression model. Zbl 0774.62070Knautz, H.; Trenkler, G. 2 1993 On the correlation between \(\overline X\) and \(S^ 2\). Zbl 0784.62047Knautz, Henning; Trenkler, Götz 1 1993 Some further results on Hermitian-matrix inequalities. Zbl 0753.15014Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz 14 1992 Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093Trenkler, G.; Toutenburg, H. 7 1992 Pre-test estimation in the linear regression model with competing linear constraints. Zbl 0770.62052Hessenius, Helga; Trenkler, Götz 1 1992 Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011Baksalary, Jerzy K.; Trenkler, Götz 29 1991 Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060Stahlecker, P.; Trenkler, G. 5 1991 Covariance adjustment in biased estimation. Zbl 0870.62042Baksalary, Jerzy K.; Trenkler, Götz 3 1991 Mean square error matrix comparisons between biased restricted least squares estimators. Zbl 0746.62065Trenkler, Götz 1 1991 Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066Trenkler, G.; Toutenburg, H. 67 1990 Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571Toutenberg, H.; Trenkler, G. 4 1990 Mean square error matrix improvements and admissibility of linear estimators. Zbl 0685.62052Baksalary, Jerzy K.; Liski, Erkki P.; Trenkler, Götz 16 1989 Mean square error matrix superiority of estimators under linear restrictions and misspecification. Zbl 1328.62452Wijekoon, P.; Trenkler, G. 4 1989 Mean square error matrix superiority of the mixed regression estimator under misspecification. Zbl 0718.62153Trenkler, Götz; Wijekoon, Pushba 2 1989 Full and partial minimax estimation in regression analysis with additional linear constraints. Zbl 0653.62053Stahlecker, P.; Trenkler, G. 10 1988 Minimax estimation with additional linear restrictions. A simulation study. Zbl 0695.62158Schipp, B.; Trenkler, G.; Stahlecker, P. 4 1988 Some remarks on a ridge-type-estimator and good prior means. Zbl 0696.62292Trenkler, Götz 4 1988 Quasi minimax-estimation in the linear regression model. Zbl 0635.62066Trenkler, G.; Stahlecker, P. 28 1987 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 599 Authors 70 Trenkler, Götz 58 Mosić, Dijana 56 Chen, Jianlong 39 Baksalary, Oskar Maria 27 Thome, Néstor 23 Benítez Lopez, Julio 23 Stahlecker, Peter 21 Liu, Xiaoji 19 Tian, Yongge 18 Gross, Jürgen 18 Stanimirović, Predrag S. 18 Xu, Sanzhang 17 Ma, Haifeng 17 Özkale, M. Revan 17 Yang, Hu 16 Deng, Chunyuan 15 Wang, Hongxing 14 Baksalary, Jerzy K. 13 Zhou, Mengmeng 12 Kaçıranlar, Selahattin 12 Li, Tingting 12 Puntanen, Simo 11 Đorđević, Dragan S. 11 Gao, Yuefeng 11 Kyrchei, Ivan I. 11 Wei, Yimin 11 Zuo, Kezheng 10 Liski, Erkki P. 10 Wei, Laisheng 10 Zhu, Huihui 9 Cvetković-Ilić, Dragana S. 9 Ferreyra, David E. 9 Patrício, Pedro 8 Malik, Saroj B. 8 Markiewicz, Augustyn 8 Ohtani, Kazuhiro 8 Özdemir, Halim 8 Toutenburg, Helge 8 Wu, Jibo 7 Akdeniz, Fikri 7 Rakočević, Vladimir 7 Wang, Dingguo 7 Wijekoon, Pushpakanthie 6 Arnold, Bernhard F. 6 Chen, Xiaofeng 6 Kibria, B. M. Golam 6 Li, Yalian 6 Marovt, Janko 6 Rakić, Dragan S. 6 Schipp, Bernhard 6 Styan, George P. H. 6 Zhou, Yukun 5 Açar, Tuğba Söküt 5 Aslam, Muhammad 5 Dawoud, Issam 5 Koliha, Jerry J. 5 Lebtahi, Leila 5 Liu, Shuangzhe 5 Özbay, Nimet 5 Schmidt, Karsten 5 Wang, Long 5 Zou, Honglin 4 Akram, Muhammad Nauman 4 Amin, Muhammad Shoib 4 Arumairajan, Sivarajah 4 Corach, Gustavo 4 Hauke, Jan 4 Hurley, Ted 4 Ke, Yuanyuan 4 Kuran, Özge 4 Lattanzi, Marina Beatriz 4 Levis, Fabián Eduardo 4 Matvejchuk, Marjan Stepanovich 4 Roozbeh, Mahdi 4 Sakallioglu, Sadullah 4 Sivakumar, Koratti Chengalrayan 4 Trenkler, Dietrich 4 Wei, Junchao 4 Zhang, WeiPing 3 Abonazel, Mohamed Reda 3 Ahmed, Syed Ejaz 3 Büning, Herbert 3 Catral, Minerva 3 Chandra, Shalini 3 Chang, Xinfeng 3 Dinčić, Nebojša Č. 3 Djikić, Marko S. 3 Dolinar, Gregor 3 Du, Hongke 3 Gonzalez, María Celeste 3 Güler, Hüseyin 3 Hernández, M. V. 3 Isotalo, Jarkko 3 Jiang, Bo 3 Kala, Radosław 3 Kişi, Emre 3 Knautz, Henning 3 Kössler, Wolfgang 3 Kuzma, Bojan 3 Lauterbach, Jörg ...and 499 more Authors all top 5 Cited in 145 Serials 91 Linear Algebra and its Applications 83 Linear and Multilinear Algebra 58 Communications in Statistics. Theory and Methods 48 Statistical Papers 35 Applied Mathematics and Computation 31 Communications in Statistics. Simulation and Computation 27 Journal of Statistical Planning and Inference 19 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 8 Communications in Algebra 8 Journal of Multivariate Analysis 8 Advances in Applied Clifford Algebras 8 Journal of Algebra and its Applications 7 International Journal of Mathematical Education in Science and Technology 7 Quaestiones Mathematicae 7 Computational and Applied Mathematics 7 ELA. The Electronic Journal of Linear Algebra 7 Journal of Applied Statistics 7 Frontiers of Mathematics in China 7 Open Mathematics 6 Aequationes Mathematicae 6 Computational Statistics and Data Analysis 6 Special Matrices 5 Indian Journal of Pure & Applied Mathematics 5 Journal of Computational and Applied Mathematics 5 Bulletin of the Malaysian Mathematical Sciences Society. 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Serie Quarta 1 The Annals of Statistics 1 Biometrical Journal 1 BIT 1 Calcolo 1 Collectanea Mathematica 1 Czechoslovak Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra 1 Journal of the Korean Mathematical Society 1 Mathematica Slovaca 1 Proceedings of the American Mathematical Society 1 Statistica Neerlandica 1 Bulletin of the Korean Mathematical Society 1 Circuits, Systems, and Signal Processing 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 American Journal of Mathematical and Management Sciences 1 Physica D 1 Facta Universitatis. Series Mathematics and Informatics 1 Machine Learning 1 Neural Computation 1 YUJOR. Yugoslav Journal of Operations Research 1 European Journal of Operational Research 1 Glasnik Matematički. Serija III 1 International Journal of Computer Mathematics 1 Russian Mathematics ...and 45 more Serials all top 5 Cited in 43 Fields 354 Linear and multilinear algebra; matrix theory (15-XX) 317 Statistics (62-XX) 79 Associative rings and algebras (16-XX) 79 Operator theory (47-XX) 56 Numerical analysis (65-XX) 32 Functional analysis (46-XX) 28 Order, lattices, ordered algebraic structures (06-XX) 14 Computer science (68-XX) 8 Operations research, mathematical programming (90-XX) 7 Probability theory and stochastic processes (60-XX) 7 Quantum theory (81-XX) 6 Group theory and generalizations (20-XX) 6 Systems theory; control (93-XX) 5 Combinatorics (05-XX) 5 Number theory (11-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 Ordinary differential equations (34-XX) 4 Mathematics education (97-XX) 3 Algebraic geometry (14-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 Partial differential equations (35-XX) 2 Difference and functional equations (39-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Fluid mechanics (76-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 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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