Testing Independence of Covariates and Errors in Non‐parametric Regression
针对非参数回归模型Y=m(X)+ε，提出了检验协变量X与误差ε是否独立的新方法，并研究了局部检验功效，模拟和实际数据表明其性能良好。
Abstract Consider a non‐parametric regression model Y = m ( X )+ ϵ , where m is an unknown regression function, Y is a real‐valued response variable, X is a real covariate, and ϵ is the error term. In this article, we extend the usual tests for homoscedasticity by developing consistent tests for independence between X and ϵ . Further, we investigate the local power of the proposed tests using Le Cam's contiguous alternatives. An asymptotic power study under local alternatives along with extensive finite sample simulation study shows that the performance of the new tests is competitive with existing ones. Furthermore, the practicality of the new tests is shown using two real data sets.