Preliminary test estimation of a vector of parametric functions in the general Gauss-Markov model

The theory of preliminary test estimation based on comparing the matrix risks of two competing estimators of β or Xβ under the general Gauss-Markov model { Y, Xβ , σ 2 V }, is extended to the situation where the interest is focused on a given vector of estimable parametric functions. Applicability o...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1993-08, Vol.36 (2), p.227-239
Main Authors: Baksalary, Jerzy K., Pordzik, Pawel R.
Format: Article
Language:English
Subjects:
block design
Exact sciences and technology
General Gauss-Markov model
Linear inference, regression
Mathematics
matrix risk
nuisance parameters
preliminary test estimation
Probability and statistics
Sciences and techniques of general use
singular linear model
Statistics
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Summary:The theory of preliminary test estimation based on comparing the matrix risks of two competing estimators of β or Xβ under the general Gauss-Markov model { Y, Xβ , σ 2 V }, is extended to the situation where the interest is focused on a given vector of estimable parametric functions. Applicability of this extension is shown in the context of a model in which Xβ=Wγ+Zδ , where γ is the vector of main parameters and δ is the vector of nuisance parameters. As an illustration, preliminary test estimation of a vector of treatment contrasts in a fixed-effect model corresponding to a block design is discussed.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(93)90126-Q