On nonparametric regression for iid observations in a general setting

• 成果类型: Article
• 署名作者: Efromovich, S
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1126-1144
• 关键词: models; RISK

摘要

we consider the problem of sharp-optimal estimation of a response function f(x) in a random design nonparametric regression under a general model where a pair of observations (Y, X) has a joint density p(y, x) = p(y\f(x))pi(x). We wish to estimate the response function with optimal minimax mean integrated squared error convergence as the sample size tends to infinity. Traditional regularity assumptions on the conditional density p(y\theta) assumed for parameter theta estimation are sufficient for sharp-optimal nonparametric risk convergence al well as for the existence of the best constant and rate of risk convergence. This best constant is a nonparametric analog of Fisher information. Many examples are sketched including location and scale families, censored data, mixture models and some well-known applied examples. A sequential approach and some aspects of experimental design are considered as well.