Sufficiency and completeness in the linear model
type: Item
instance of: scholarly article
title: Sufficiency and completeness in the linear model
zbMATH Open document ID: 0614.62080
DOI: 10.1016/0047-259X(87)90008-X
author: Jochen Mueller
published in: Journal of Multivariate Analysis
publication date: 1987-01-01T00:00:00Z
review text: The author considers first the linear model \(Ey=X\beta\), Cov y\(=V\) and defines, following \textit{J. K. Baksalary} and \textit{R. Kala} [Ann. Stat. 9, 913-916 (1981; Zbl 0471.62067)] and the reviewer [Sankhyā, Ser. A 45, 88-98 (1983; Zbl 0535.62007)], when a linear statistic \(z=Ly\) is linearly sufficient or linearly complete. New characterizations for there concepts are given (Proposition 3.1). Next, the model \(Ey=X\beta\), Cov y\(=\sigma^ 2V\) is dealt with. It is defined and characterizations are given when (Ly,y'Ty) is quadratically sufficient. As an application the author discusses stepwise regression and gives a necessary and sufficient condition when the first step estimators of expectation and residual variance, respectively, form, together with additional observations, a quadratically sufficient statistic.
reviewed by: Hilmar Drygas
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62B05
zbMATH DE Number: 3994798
zbMATH Keywords: linear prediction
zbMATH Keywords: sufficiency under normality
zbMATH Keywords: linear model
zbMATH Keywords: linear statistic
zbMATH Keywords: linearly sufficient
zbMATH Keywords: linearly complete
zbMATH Keywords: characterizations
zbMATH Keywords: stepwise regression
zbMATH Keywords: quadratically sufficient statistic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3994798