This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

中文翻译：

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变量误差模型的规范测试

本文考虑了具有变量误差的回归模型的规格测试，并提出了一个测试统计量，比较基于反卷积技术的参数拟合和非参数拟合之间的距离。与 Hall 和 Ma (2007,统计年鉴, 35, 2620–2638) 和宋 (2008,多元分析杂志, 99, 2406–2443)，我们的测试允许一般的非线性回归模型并具有互补的局部功率特性。我们为普通和超光滑测量误差密度建立了我们的检验统计量的渐近特性。仿真结果证实了我们的理论发现：我们的测试在检测高频替代方案方面具有优势，并且在某些规格下主导了现有测试。