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June 2008 Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models
Snigdhansu Chatterjee, Partha Lahiri, Huilin Li
Ann. Statist. 36(3): 1221-1245 (June 2008). DOI: 10.1214/07-AOS512

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(d3n−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.

Citation

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Snigdhansu Chatterjee. Partha Lahiri. Huilin Li. "Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models." Ann. Statist. 36 (3) 1221 - 1245, June 2008. https://doi.org/10.1214/07-AOS512

Information

Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1360.62378
MathSciNet: MR2418655
Digital Object Identifier: 10.1214/07-AOS512

Subjects:
Primary: 62D05
Secondary: 62F25 , 62F40

Keywords: bootstrap , coverage accuracy , linear mixed model , prediction interval , predictive distribution , small area

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • June 2008
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