A new adjusted maximum likelihood method for the Fay-Herriot small area model

Masayo Yoshimori, Partha Lahiri

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


In the context of the Fay-Herriot model, a mixed regression model routinely used to combine information from various sources in small area estimation, certain adjustments to a standard likelihood (e.g., profile, residual, etc.) have been recently proposed in order to produce strictly positive and consistent model variance estimators. These adjustments protect the resulting empirical best linear unbiased prediction (EBLUP) estimator of a small area mean from the possible over-shrinking to the regression estimator. However, in certain cases, the existing adjusted likelihood methods can lead to high biases in the estimation of both model variance and the associated shrinkage factors and can even produce a negative second-order unbiased mean square error (MSE) estimate of an EBLUP. In this paper, we propose a new adjustment factor that rectifies the above-mentioned problems associated with the existing adjusted likelihood methods. In particular, we show that our proposed adjusted residual maximum likelihood and profile maximum likelihood estimators of the model variance and the shrinkage factors enjoy the same higher-order asymptotic bias properties of the corresponding residual maximum likelihood and profile maximum likelihood estimators, respectively. We compare performances of the proposed method with the existing methods using Monte Carlo simulations.

Original languageEnglish
Pages (from-to)281-294
Number of pages14
JournalJournal of Multivariate Analysis
Publication statusPublished - Feb 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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