Small area estimation via heteroscedastic nested-error regression

Jiming Jiang, Thuan Nguyen

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We show that the maximum likelihood estimators (MLEs) of the fixed effects and within-cluster correlation are consistent in a heteroscedastic nested-error regression (HNER) model with completely unknown within-cluster variances under mild conditions. The result implies that the empirical best linear unbiased prediction (EBLUP) method for small area estimation is valid in such a case. We also show that ignoring the heteroscedasticity can lead to inconsistent estimation of the within-cluster correlation and inferior predictive performance. A jackknife measure of uncertainty for the EBLUP is developed under the HNER model. Simulation studies are carried out to investigate the finite-sample performance of the EBLUP and MLE under the HNER model, with comparisons to those under the nested-error regression model in various situations, as well as that of the jackknife measure of uncertainty. The well-known Iowa crops data is used for illustration.

Original languageEnglish (US)
Pages (from-to)588-603
Number of pages16
JournalCanadian Journal of Statistics
Volume40
Issue number3
DOIs
StatePublished - Sep 1 2012

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Keywords

  • Consistency
  • EBLUP
  • Heteroscedasticity
  • Jackknife MSPE estimator
  • Maximum likelihood estimation
  • Nuisance parameters
  • Small area estimation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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