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NONPARAMETRIC SIGNIFICANCE TESTING IN MEASUREMENT ERROR MODELS
Published online by Cambridge University Press: 04 June 2021
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.
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- © The Author(s), 2021. Published by Cambridge University Press
Footnotes
The authors would like to thank the Editor, Associate Editor, three anonymous referees, Karun Adusumilli, Taisuke Otsu, Ricardo Reis, and Peter Robinson for helpful comments. Financial support from the SMU Dedman College Research Fund (12-412268; Dong), and the Aarhus University Research Fund (AUFF-26852; Taylor) is gratefully acknowledged.