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 language | English (US) |
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Pages (from-to) | 588-603 |
Number of pages | 16 |
Journal | Canadian Journal of Statistics |
Volume | 40 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2012 |
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