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Trimmed estimates in simultaneous estimation of parameters in exponential families. (English) Zbl 0543.62003

Let \(X_ 1,...X_ p\) be p independent random variables with \(p\geq 3\) where each \(X_ i\) has a distribution belonging to the one-parameter exponential family. The problem considered is the simultaneous estimation of parameters in the presence of extreme observations. The authors extend the ideas of C. Stein [Ann. Stat. 9, 1135-1151 (1981; Zbl 0476.62035)] to obtain trimmed versions of several estimators of the natural parameter.
The important special cases of the Poisson and negative binomial in the discrete exponential case and normal and gamma distribution in the continuous exponential case are considered in detail. Some numerical results on the risk of the shrinkage are presented for Poisson and gamma distributions.
Reviewer: B.L.S.Prakasa Rao

MSC:

62C15 Admissibility in statistical decision theory
62H12 Estimation in multivariate analysis

Citations:

Zbl 0476.62035
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References:

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