ON DIFFERENTIABLE FUNCTIONALS

• 成果类型: Article
• 署名作者: VANDERVAART, A
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1991
• 页码: 178-204
• 关键词: information

摘要

Given a sample of size n from a distribution P-lambda, one wants to estimate a functional psi(lambda) of the (typically infinite-dimensional) parameter lambda. Lower bounds on the performance of estimators can be based on the concept of a differentiable functional P-lambda --> psi(lambda). In this paper we relate a suitable definition of differentiable functional to differentiability of lambda --> dP-lambda-1/2 and lambda --> psi(lambda). Moreover, we show that regular estimability of a functional implies its differentiability.