NONPARAMETRIC SIGNIFICANCE TESTING IN MEASUREMENT ERROR MODELS

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