Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

Projection-based Consistent Test for Linear Regression Model with Missing Response and Covariates

In recent years,there has been a large amount of literature on missing data.Most of them focus on situations where there is only missingness in response or covariate.In this paper,we consider the adequacy check for the linear regression model with the response and covariates missing simultaneously.We apply model adjustment and inverse probability weighting methods to deal with the missingness of response and covariate,respectively.In order to avoid the curse of dimension,we propose an empirical process test with the linear indicator weighting function.The asymptotic properties of the proposed test under the null,local and global alternative hypothe tical models are rigorously investigated.A consisten t wild boot strap method is developed to approximate the critical value.Finally,simulation studies and real data analysis are performed to show that the proposed method performed well.

Empirical Likelihood Based Diagnostics for Heteroscedasticity in Semiparametric Varying-Coefficient Partially Linear Models with Missing Responses

This paper proposes an empirical likelihood based diagnostic technique for heteroscedasticity for semiparametric varying-coefficient partially linear models with missing responses. Firstly, the authors complement the missing response variables by regression method. Then, the empirical likelihood method is introduced to study the heteroscedasticity of the semiparametric varying-coefficient partially linear models with complete-case data. Finally, the authors obtain the finite sample property by numerical simulation.

Empirical likelihood for single-index models with responses missing at random

The missing response problem in single-index models is studied, and a bias-correction method to infer the index coefficients is developed. Two weighted empirical log-likelihood ratios with asymptotic chisquare are derived, and the corresponding empirical likelihood confidence regions for the index coefficients are constructed. In addition, the estimators of the index coefficients and the link function are defined, and their asymptotic normalities are proved. A simulation study is conducted to compare the empirical likelihood and the normal approximation based method in terms of coverage probabilities and average lengths of confidence intervals. A real example illustrates our methods.

Empirical Likelihood Method for Quantiles with Response Data Missing at Random

Empirical likelihood is a nonparametric method for constructing confidence intervals and tests, notably in enabling the shape of a confidence region determined by the sample data. This paper presents a new version of the empirical likelihood method for quantiles under kernel regression imputation to adapt missing response data. It eliminates the need to solve nonlinear equations, and it is essy to apply. We also consider exponential empirical likelihood as an alternative method. Numerical results are presented to compare our method with others.