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Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices

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  • Kojima, Masahiro
  • Kubokawa, Tatsuya

Abstract

Consider the problem of testing a linear hypothesis of regression coefficients in a general linear regression model with a covariance matrix involving several nuisance parameters. Then, the Bartlett-type adjustments of the Wald, Score, and modified Likelihood Ratio tests are derived for general consistent estimators of the unknown nuisance parameters. The adjusted test statistics have second-order corrections in type I errors. Simple parametric bootstrap methods are also suggested for estimating the Bartlett-type adjustments and it is shown that they have the second order accuracy.

Suggested Citation

  • Kojima, Masahiro & Kubokawa, Tatsuya, 2013. "Bartlett-type adjustments for hypothesis testing in linear models with general error covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 162-174.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:162-174
    DOI: 10.1016/j.jmva.2013.07.016
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    1. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Rayner, Robert K., 1990. "Bartlett's correction and the bootstrap in normal linear regression models," Economics Letters, Elsevier, vol. 33(3), pages 255-258, July.
    3. Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-842, July.
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