The Annals of Statistics

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

Peter Hall and Tapabrata Maiti

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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.

Article information

Ann. Statist., Volume 34, Number 4 (2006), 1733-1750.

First available in Project Euclid: 3 November 2006

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Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators 62J99: None of the above, but in this section

Best linear unbiased predictor bias reduction bootstrap deconvolution double bootstrap empirical predictor mean-squared error mixed effects moment-matching bootstrap small-area inference two-stage estimation wild bootstrap


Hall, Peter; Maiti, Tapabrata. Nonparametric estimation of mean-squared prediction error in nested-error regression models. Ann. Statist. 34 (2006), no. 4, 1733--1750. doi:10.1214/009053606000000579.

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