Efficient estimation of integral functionals of a density

• 成果类型: Article
• 署名作者: Laurent, B
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 659-681
• 关键词: derivatives

摘要

We consider the problem of estimating a functional of a density of the type integral phi(f,.). Starting from efficient estimators of linear and quadratic functionals of f and using a Taylor expansion of phi, we build estimators that achieve the n(-1/2) rate whenever if is smooth enough. Moreover, we show that these estimators are efficient. Concerning the estimation of quadratic functionals (more precisely, of integrated squared density) Bickel and Ritov have already built efficient estimators. We propose here an alternative construction based on projections, which seems more natural.