SIMULTANEOUS ESTIMATION IN DISCRETE MULTIVARIATE EXPONENTIAL-FAMILIES

• 成果类型: Article
• 署名作者: CHOU, JP
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176347984
• 发表日期: 1991
• 页码: 314-328
• 关键词: poisson

摘要

Let X have a discrete density of the form f(x) = t(x)xi(theta)theta-1(x1) ... theta-p(x)p, where t(x) is nonzero on some infinite subset of Z(p). Consider simultaneous estimation of the theta-i under the loss L(m) (theta, delta) = SIGMA-i(p) = 1 theta-i-m (theta-i - delta-i)2, m greater-than-or-equal-to 0. For integers m greater-than-or-equal-to 1, estimators are found which improve on the maximum likelihood estimator or uniformly minimum variance unbiased estimator. The improved estimators are distinguished by the property that they do not depend on m for large values of the observed vector. On the other hand, we prove admissibility of a class of estimators, including the MLE and UMVUE, for some discrete densities of the indicated form under squared error loss (m = 0).