SPECIFICATION TESTING FOR ERRORS-IN-VARIABLES MODELS
针对变量含误差的回归模型，提出一种基于反卷积技术的设定检验统计量，通过比较参数与非参数拟合的距离来检验模型设定，适用于一般非线性模型，并在高频备择假设下具有优势。
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.