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Nonparametric estimation of mean-squared prediction error in nested-error regression models. (English) Zbl 1246.62106
Summary: 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 the mean-squared prediction error is the main way in which prediction performance is measured. We suggest a new approach to estimating the 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 the errors. Additionally, it is simple and easy to apply. This is achieved through using Monte Carlo simulations to implicitly develop formulae which, in a more conventional approach, would be derived laboriously by mathematical arguments.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62G09 Nonparametric statistical resampling methods 62G05 Nonparametric estimation 65C05 Monte Carlo methods
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