Information theory and superefficiency

• 成果类型: Article
• 署名作者: Barron, A; Hengartner, N
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1800-1825
• 关键词: Complexity

摘要

The asymptotic risk of efficient estimators with Kullback-Leibler loss in smoothly parametrized statistical models is k/2n, where k is the parameter dimension and n is the sample size. Under fairly general conditions, we given a simple information-theoretic proof that the set of parameter values where any arbitrary estimator is superefficient is negligible. The proof is based on a result of Rissanen that codes have asymptotic redundancy not smaller than (k/2)log n, except in a set of measure 0.