Isotalo, Jarkko; Puntanen, Simo Linear sufficiency and completeness in the partitioned linear model. (English) Zbl 1133.62338 Acta Comment. Univ. Tartu. Math. 10, 53-67 (2006). Summary: We consider the estimation of \({\mathbf X}_1\beta_1\) under the partitioned linear model \(\{{\mathbf y},{\mathbf X}_1\beta_1+ {\mathbf X}_2\beta_2, \sigma^2{\mathbf V}\}\). In particular, we consider linear sufficiency and linear completeness of \({\mathbf X}_1\beta_1\). We give new characterizations for linear sufficiency of \({\mathbf X}_1\beta_1\), and define and characterize linear completeness in a case of estimation of \({\mathbf X}_1\beta_1\). We also introduce a predictive approach for obtaining the best linear unbiased estimator of \({\mathbf X}_1\beta_1\), and subsequently, we give linear analogues of the Rao-Blackwell and Lehmann-Scheffé theorems in the context of estimating \({\mathbf X}_1\beta_1\). Cited in 6 Documents MSC: 62J05 Linear regression; mixed models 62B05 Sufficient statistics and fields 62H12 Estimation in multivariate analysis Keywords:best linear unbiased estimation; Gauss-Markov model; linear sufficiency; linear completeness; linear estimation PDFBibTeX XMLCite \textit{J. Isotalo} and \textit{S. Puntanen}, Acta Comment. Univ. Tartu. Math. 10, 53--67 (2006; Zbl 1133.62338)