| Model validation for regression with complex data is an important topic in statistics.In this article,we study model checking when data is censored or with measurement error.This paper is divided into two parts.In the first part,we investigate the adequacy check of the parametric Tobit model.Firstly,based on the estimated cumulative residuals,we construct a Cramer-von Mises type of test statistic.The asymptotic properties of the test statistic under the null hypothe-sis are rigorously investigated.It is shown that the proposed method is consistent.Meanwhile,it avoids the nonparametric smoothing and the choice of smoothing parameter,and it is free of the distribution specification of the response variable,covariates and model error.Secondly,simu-lation studies are conducted to evaluate the numerical performance of the proposed test method by comparing them with the existing testing.The salary data is analyzed to validate the effect of the proposed method.In the second part,we consider the adequacy check of errors-in variables varying-coefficient model when replicate measurements are available.Firstly,We calibrate the estimator of the regression coefficients directly and construct an empirical process based testing method by employing the estimated cumulative residuals.The asymptotic properties of the test statistic under the null hypothesis,local and global alternatives are rigorously investigated.It is shown that the proposed method has the asymptotic power one for the alternative hypothetical models which close to the null hypothesis at the rate slower than the rate for parametric part..It is also shown that the proposed test can detect the Pitman alternative models.Secondly,by theoretical and numerical studies,we illustrate that the naive method,which ignores the mea-surement error,cannot control Type I error and therefore is uselessness.Simulation studies and real data analyses reveal that proposed test performs satisfactorily. |
PDF Full Text Request