NONEXISTENCE OF INFORMATIVE UNBIASED ESTIMATORS IN SINGULAR PROBLEMS

• 成果类型: Article
• 署名作者: LIU, RC; BROWN, LD
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349012
• 发表日期: 1993
• 页码: 1-13
• 关键词: geometrizing rates; CONVERGENCE; point

摘要

In many nonparametric problems, such as density estimation, nonparametric regression and so on, all the existing informative estimators are biased (asymptotic or finite sample). There has long been a suspicion that either informative unbiased estimators do not exist for such problems or they must be quite complicated. In this paper, we clarify the nonexistence of informative unbiased estimators in all singular problems both for fixed sample size and asymptotically (this includes most problems with optimal rate of convergence slower than n-1/2). We also discuss situations in regular problems where such nonexistences can occur.