×

Admissible minimax model selection rule. (English) Zbl 0631.62007

This paper considers the problem of choosing one between the simple model \(N(0,I_ d)\) and the full model \(N(\theta,I_ d)\) based on the observation X from \(N(\theta,I_ d)\) where \(X,\theta \in R^ d\), 0 is the null vector in \(R^ d\) and \(I_ d\) is the \(d\times d\) identity matrix. It is shown that the selection rule which chooses the full model if \(| x| >a_ 0\), for some \(a_ 0>0\), and the simple model otherwise is an admissible minimax model selection rule relative to a loss function which takes into account both inaccuracy and complexity.

MSC:

62C20 Minimax procedures in statistical decision theory
62C15 Admissibility in statistical decision theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Dempster A. P, Model searching and estimation in the logic of inference (with discussion) 56-81, in Foundations in Statistical Inference (1971)
[2] Kiefer, J. Pages 139-142 in The Future of Statistics. Academic Press.
[3] Lehmann E. L, Testing Statistical Hypotheses (1959)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.