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

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

2005-09-21

arxiv.org/abs/math/0509493v3

Annals of Statistics 2006, Vol. 34, No. 4, 1733-1750

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000579 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000579

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.

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