Zhihua Sun

Model checking for partially linear models with missing responses at random

In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data.

Improved model checking methods for parametric models with responses missing at random

In this paper, we consider the lack-of-fit test of a parametric model when the response variable is missing at random. The popular imputation and inverse probability weighting methods are first employed to tackle the missing data. Then by employing the projection technique, we propose empirical-process-based testing methods to check the appropriateness of the parametric model. The asymptotic properties of the test statistics are obtained under the null and local alternative hypothetical models. It is shown that the proposed testing methods are consistent, and can detect local alternative hypothetical models converging to the null model at the parametric rate. To determine the critical values, a consistent bootstrap method is proposed, and its asymptotic properties are established. The simulation results show that the tests outperform the existing methods in terms of empirical sizes and powers, especially under the situation with high dimensional covariates. Analysis of a diabetes data set of Pima Indians is carried out to demonstrate the application of the testing procedures.

Consistent test for parametric models with right-censored data using projections

In the literature, there are several methods to test the adequacy of parametric models with right-censored data. However, these methods will lose effect when the predictors are medium-high dimensional. In this study, a projection-based test method is built, which acts as if the predictors were scalar even if they are multidimensional. The proposed test is shown to be consistent and can detect the alternative hypothesis converging to the null hypothesis at the rate n−r with 0≤r≤1∕2. Also, it is free from the choices of the subjective parameters such as bandwidth, kernel and weighting function. A wild bootstrap method is developed to determine the critical value of the test, which is shown to be robust to the model conditional heteroskedasticity. Simulation studies and real data analyses are conducted to validate the finite sample behavior of the proposed method.

Kernel-based global MLE of partial linear random effects models for longitudinal data

ABSTRACT Random effects models have been playing a critical role for modelling longitudinal data. However, there are little studies on the kernel-based maximum likelihood method for semiparametric random effects models. In this paper, based on kernel and likelihood methods, we propose a pooled global maximum likelihood method for the partial linear random effects models. The pooled global maximum likelihood method employs the local approximations of the nonparametric function at a group of grid points simultaneously, instead of one point. Gaussian quadrature is used to approximate the integration of likelihood with respect to random effects. The asymptotic properties of the proposed estimators are rigorously studied. Simulation studies are conducted to demonstrate the performance of the proposed approach. We also apply the proposed method to analyse correlated medical costs in the Medical Expenditure Panel Survey data set.

A consistent model specification test for a partial linear model with covariates missing at random

In this paper, we discuss the model checking problem for a partial linear model when some covariates are missing at random. A weighted model-adjustment method is applied to estimate the regression coefficients and the nonparametric function for the null hypothetical partial linear model. A testing procedure based on a residual-marked empirical process is developed to check the adequacy of the partial linear model. It is shown that the proposed test is consistent and can detect the local alternatives converging to the null hypothetical model at the rate n −1/2. Since the asymptotic null distribution of the testing statistics is case-dependent, an adjusted wild bootstrap method is used to decide the critical value, which is proved to be consistent. A simulation study and a real data analysis are conducted to show that the proposed procedure works well.