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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.

MSC:

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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