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.

我们为回归模型中具有经典测量误差的回归模型开发了第一个非参数显着性检验。特别是，原假设 $E\left [Y|X^{*},Z^{*}\right ]=E\left [Y|X^{的 Cramér-von Mises 检验和 Kolmogorov-Smirnov 检验*}\right ]$ 在只有 $X^{*}$ 和 $Z^{*}$ 的噪声测量 可用时提出。推导了检验统计量的渐近零分布，并采用自举法获得临界值。尽管使用反卷积估计器构建了测试统计量，但我们表明该测试可以检测到在 $\sqrt {n}$ 处收敛到零的一系列局部替代方案-速度。我们还通过蒙特卡洛研究强调了测试的有限样本性能。