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Nonparametric Significance Testing In Measurement Error Models

Author

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  • Dong, Hao
  • Taylor, Luke

Abstract

We develop the first nonparametric significance test for regression models with classical measurement error in the regressors. In particular, a Cramér-von Mises test and a Kolmogorov–Smirnov test for the null hypothesis $E\left [Y|X^{*},Z^{*}\right ]=E\left [Y|X^{*}\right ]$ 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 $\sqrt {n}$ -rate. We also highlight the finite sample performance of the test through a Monte Carlo study.

Suggested Citation

  • Dong, Hao & Taylor, Luke, 2022. "Nonparametric Significance Testing In Measurement Error Models," Econometric Theory, Cambridge University Press, vol. 38(3), pages 454-496, June.
    • Handle: RePEc:cup:etheor:v:38:y:2022:i:3:p:454-496_2
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    Cited by:

    1. Xiaojun Song & Jichao Yuan, 2025. "Specification tests for regression models with measurement errors," Papers 2511.04127, arXiv.org.

    More about this item

    JEL classification:

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

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