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Nonparametric Significance Testing in Measurement Error Models

Author

Listed:
  • Hao Dong

    (Southern Methodist University)

  • Luke Taylor

    (Aarhus University)

Abstract

We develop the first nonparametric significance test for regression models with classical measurement error in the regressors. In particular, the Cram�r-von Mises test and the Kolmogorov-Smirnov test for the null hypothesis $E[Y|X^{*},Z^{*}]=E[Y|Z^{*}]$ are proposed when only noisy measurements of $X^{*}$ and $Z^{*}$ are available. The asymptotic null distributions of the test statistics are derived and a bootstrap method is implemented to obtain the critical values. Despite the test statistics being constructed using deconvolution estimators, we show that the test can detect a sequence of local alternatives converging to the null at the root-n rate. We also highlight the finite sample performance of the test through a Monte Carlo study.

Suggested Citation

  • Hao Dong & Luke Taylor, 2020. "Nonparametric Significance Testing in Measurement Error Models," Departmental Working Papers 2003, Southern Methodist University, Department of Economics.
    • Handle: RePEc:smu:ecowpa:2003
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    References listed on IDEAS

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    More about this item

    Keywords

    Significance test; deconvolution; classical measurement error; unknown error distribution.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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