Nonparametric estimation of mean-squared prediction error in nested-error regression models

• 成果类型: Article
• 署名作者: Hall, Peter; Maiti, Tapabrata
• 署名单位: Australian National University; Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000579
• 发表日期: 2006
• 页码: 1733-1750
• 关键词: standard errors; Optimal Rates; deconvolution; CONVERGENCE; density

摘要

Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and mean-squared prediction error is the main way in which prediction performance is measured. In this paper we suggest a new approach to estimating mean-squared prediction error. We introduce a matched-moment, double-bootstrap algorithm, enabling the notorious underestimation of the naive mean-squared error estimator to be substantially reduced. Our approach does not require specific assumptions about the distributions of errors. Additionally, it is simple and easy to apply. This is achieved through using Monte Carlo simulation to implicitly develop formulae. which, in a more conventional approach, would be derived laboriously by mathematical arguments.