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Model checking in errors-in-variables regression

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  • Song, Weixing

Abstract

This paper discusses a class of minimum distance tests for fitting a parametric regression model to a class of regression functions in the errors-in-variables model. These tests are based on certain minimized distances between a nonparametric regression function estimator and a deconvolution kernel estimator of the conditional expectation of the parametric model being fitted. The paper establishes the asymptotic normality of the proposed test statistics under the null hypothesis and that of the corresponding minimum distance estimators. We also prove the consistency of the proposed tests against a fixed alternative and obtain the asymptotic distributions for general local alternatives. Simulation studies show that the testing procedures are quite satisfactory in the preservation of the finite sample level and in terms of a power comparison.

Suggested Citation

  • Song, Weixing, 2008. "Model checking in errors-in-variables regression," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2406-2443, November.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2406-2443
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    References listed on IDEAS

    as
    1. Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
    2. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Otsu, Taisuke & Taylor, Luke, 2021. "Specification Testing For Errors-In-Variables Models," Econometric Theory, Cambridge University Press, vol. 37(4), pages 747-768, August.
    3. Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    4. Song, Weixing, 2009. "Lack-of-fit testing in errors-in-variables regression model with validation data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 765-773, March.
    5. Sun, Zhihua & Ye, Xue & Sun, Liuquan, 2015. "Consistent test of error-in-variables partially linear model with auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 118-131.
    6. Chuanlong Xie & Lixing Zhu, 2018. "A minimum projected-distance test for parametric single-index Berkson models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 700-715, September.

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