Estimation of a loss function for spherically symmetric distributions in the general linear model. (English) Zbl 0829.62011

Summary: This paper is concerned with estimating the loss of a point estimator when sampling from a spherically symmetric distribution. We examine the canonical setting of a general linear model where the dimension of the parameter space is greater than 4 and less than the dimension of the sampling space.
We consider two location estimators – the least squares estimator and a shrinkage estimator – and we compare their unbiased loss estimator with an improved loss estimator. The domination results are valid for a large class of spherically symmetric distributions and, in so far as the sampling distribution does not need to be precisely specified, the estimates have desirable robustness properties.


62C05 General considerations in statistical decision theory
62C99 Statistical decision theory
62F35 Robustness and adaptive procedures (parametric inference)
62H12 Estimation in multivariate analysis
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