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

Snigdhansu Chatterjee, Partha Lahiri, Huilin Li

Research output: Contribution to journalArticle

45 Citations (Scopus)

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 0(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.

Original languageEnglish (US)
Pages (from-to)1221-1245
Number of pages25
JournalAnnals of Statistics
Volume36
Issue number3
DOIs
StatePublished - Jun 1 2008

Fingerprint

Best Linear Unbiased Prediction
Parametric Bootstrap
Linear Mixed Model
Prediction Interval
Prediction Error
Approximation
Mean Squared Error
Coverage
Estimate
Interpretability
Bootstrap
Histogram
Entire
Prediction interval
Mixed model
Prediction
Parametric bootstrap
Demonstrate
Simulation

Keywords

  • Bootstrap
  • Coverage accuracy
  • Linear mixed model
  • Prediction interval
  • Predictive distribution
  • Small area

Cite this

Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models. / Chatterjee, Snigdhansu; Lahiri, Partha; Li, Huilin.

In: Annals of Statistics, Vol. 36, No. 3, 01.06.2008, p. 1221-1245.

Research output: Contribution to journalArticle

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