The Poisson Compound Decision Problem Revisited

• 成果类型: Article
• 署名作者: Brown, Lawrence D.; Greenshtein, Eitan; Ritov, Ya'acov
• 署名单位: University of Pennsylvania; Hebrew University of Jerusalem
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.771582
• 发表日期: 2013
• 页码: 741-749
• 关键词: nonparametric empirical bayes; estimator

摘要

The compound decision problem for a vector of independent Poisson random variables with possibly different means has a half-century-old solution. However, it appears that the classical solution needs smoothing adjustment. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem. A simulation study shows the effectiveness of the procedures in improving the performance over that of the classical procedure. A real data example is also provided. The procedures depend on a smoothness parameter that can be selected using a nonstandard cross-validation step, which is of independent interest. Finally, we mention some asymptotic results.