Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models

Abstract

Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only $O(d^3{n}^{-3/2})$, where $d$ is the number of parameters and $n$ the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.

Published in at http://dx.doi.org/10.1214/07-AOS512 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Mean squared error of empirical predictor
• Improved minimax predictive densities under Kullback--Leibler loss
• Nonparametric estimation of mean-squared prediction error in nested-error regression models
• Shrinkage priors for Bayesian prediction

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• Discussion of "Estimating Random Effects via Adjustment for Density Maximization" by C. Morris and R. Tang
• Small Area Estimation using EBLUPs under the Nested Error Regression Model
• Empirical Best Linear Unbiased Predictors in Multivariate Nested-Error Regression Models
• Transforming response values in small area prediction
• Estimation and Prediction in Transformed Nested Error Regression Models
• Parametric Bootstrap Confidence Intervals for the Multivariate Fay-Herriot Model
• Adaptively Transformed Mixed Model Prediction of General Finite Population Parameters
• Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval