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Distribution-free lack-of-fit tests in balanced mixed models

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  • Song, Weixing
  • Du, Juan

Abstract

Here we discuss the problem of fitting a parametric model to the regression function of the fixed effects in a class of balanced mixed effects models. The proposed test is based on the supremum of the Khmaladze transformation of a certain partial sum process of calibrated residuals, and the asymptotic null distribution of this transformed process turns out to be the same as that of a time transformed standard Brownian motion. Moreover, we show that this test is consistent against a large class of fixed alternatives and has non-trivial asymptotic power against a class of nonparametric local alternatives. Simulation studies are conducted to assess the finite sample performance of the proposed test.

Suggested Citation

  • Song, Weixing & Du, Juan, 2010. "Distribution-free lack-of-fit tests in balanced mixed models," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1378-1387, September.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1378-1387
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    References listed on IDEAS

    as
    1. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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