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Model checking for general linear error-in-covariables model with validation data

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Abstract

In this paper, model checking problem is considered for general linear model when covariables are measured with error and an independent validation data set is available. Without assuming any error model structure between the true variable and the surrogate variable, the author first apply nonparametric method to model the relationship between the true variable and the surrogate variable with the help of the validation sample. Then the author construct a score-type test statistic through model adjustment. The large sample behaviors of the score-type test statistic are investigated. It is shown that the test is consistent and can detect the alternative hypothesis close to the null hypothesis at the rate n −r with 0 ≤ r ≤ 1/2. Simulation results indicate that the proposed method works well.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Pengjie Dai & Zhihua Sun

  2. School of Business, Renmin University of China, Beijing, 100872, China

    Pengjie Dai

  3. School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhihua Sun

  4. Department of Mathematics, Beijing Forestry University, Beijing, 100083, China

    Peng Wang

Authors
  1. Pengjie Dai
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  2. Zhihua Sun
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  3. Peng Wang
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Corresponding author

Correspondence to Zhihua Sun.

Additional information

This research is supported by the National Natural Science Foundation of China (10901162, 10926073), the President Fund of GUCAS and China Postdoctoral Science Foundation.

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Dai, P., Sun, Z. & Wang, P. Model checking for general linear error-in-covariables model with validation data. J Syst Sci Complex 23, 1153–1166 (2010). https://doi.org/10.1007/s11424-010-8051-7

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  • DOI: https://doi.org/10.1007/s11424-010-8051-7

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