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A consistent model specification test for a partial linear model with covariates missing at random

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  • Tianfa Xie
  • Zhihua Sun
  • Liuquan Sun

Abstract

In this paper, we discuss the model checking problem for a partial linear model when some covariates are missing at random. A weighted model-adjustment method is applied to estimate the regression coefficients and the nonparametric function for the null hypothetical partial linear model. A testing procedure based on a residual-marked empirical process is developed to check the adequacy of the partial linear model. It is shown that the proposed test is consistent and can detect the local alternatives converging to the null hypothetical model at the rate n -super- - 1/2. Since the asymptotic null distribution of the testing statistics is case-dependent, an adjusted wild bootstrap method is used to decide the critical value, which is proved to be consistent. A simulation study and a real data analysis are conducted to show that the proposed procedure works well.

Suggested Citation

  • Tianfa Xie & Zhihua Sun & Liuquan Sun, 2012. "A consistent model specification test for a partial linear model with covariates missing at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 841-856, December.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:841-856
    DOI: 10.1080/10485252.2012.712692
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
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    6. Sun, Zhihua & Wang, Qihua & Dai, Pengjie, 2009. "Model checking for partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 636-651, April.
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