The Annals of Statistics

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

Peter Hall and Tapabrata Maiti

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 3 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1162567631

Digital Object Identifier
doi:10.1214/009053606000000579

Mathematical Reviews number (MathSciNet)
MR2283715

Zentralblatt MATH identifier
1246.62106

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

Keywords
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

Citation

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. https://projecteuclid.org/euclid.aos/1162567631


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