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

Masayo Yoshimori, Partha Lahiri

研究成果: Contribution to journalArticle査読

23 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)281-294
ページ数14
ジャーナルJournal of Multivariate Analysis
124
DOI
出版ステータス出版済み - 2 2014
外部発表はい

All Science Journal Classification (ASJC) codes

  • 統計学および確率
  • 数値解析
  • 統計学、確率および不確実性

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