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Bartlett-type Correction of the Generalized Least Squares Test in the Fay-Herriot Model

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

Consider the problem of testing the linear hypothesis on the regression coefficients in the Fay-Herriot model which has been used in the small area problem. Since this model involves the random effects, a test based on the generalized least squares estimator, called the GLS test, depends on the estimate of the 'between' component of variance, which causes the problem that it has an inflated type I error (size) when the variance component is far from zero. To fix this problem, we derive the second order approximation of the distribution of the GLS test statistic under the null hypothesis. Using the Bartlett-type correction, we obtain modified test statistics with sizes identical to the nominal significance level in the second-order asymptotic. As estimators of the variance component, the Prasad-Rao estimator, Fay-Herriot estimator, maximum likelihood (ML) estimator and the restricted maximum likelihood (REML) estimator are used and the corresponding modified tests based on the Bartlett-type correction are given. The sizes of these tests are investigated numerically and the Bartlett-type correction is shown to work well.

Suggested Citation

  • Tatsuya Kubokawa, 2008. "Bartlett-type Correction of the Generalized Least Squares Test in the Fay-Herriot Model," CIRJE F-Series CIRJE-F-590, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2008cf590
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