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Specification testing for errors-in-variables models

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  • Otsu, Taisuke
  • Taylor, Luke

Abstract

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620-2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406-2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

Suggested Citation

  • Otsu, Taisuke & Taylor, Luke, 2020. "Specification testing for errors-in-variables models," LSE Research Online Documents on Economics 102690, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:102690
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    References listed on IDEAS

    as
    1. 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.
    2. repec:adr:anecst:y:2006:i:81:p:02 is not listed on IDEAS
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    Cited by:

    1. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2021. "Average Derivative Estimation Under Measurement Error," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1004-1033, October.
    2. Kato, Kengo & Sasaki, Yuya, 2019. "Uniform confidence bands for nonparametric errors-in-variables regression," Journal of Econometrics, Elsevier, vol. 213(2), pages 516-555.
    3. Dong, Hao & Otsu, Taisuke & Taylor, Luke, 2022. "Estimation of varying coefficient models with measurement error," Journal of Econometrics, Elsevier, vol. 230(2), pages 388-415.
    4. Daisuke Kurisu & Taisuke Otsu, 2019. "On the uniform convergence of deconvolution estimators from repeated measurements," STICERD - Econometrics Paper Series 604, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. Kurisu, Daisuke & Otsu, Taisuke, 2022. "On the uniform convergence of deconvolution estimators from repeated measurements," LSE Research Online Documents on Economics 107533, London School of Economics and Political Science, LSE Library.

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    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

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