Estimation and empirical likelihood for single-index models with missing data in the covariates

The estimation and empirical likelihood for single-index models with missing covariates are studied. A generalized estimating equations estimator for index coefficients with missing covariates is constructed, and its asymptotic distribution is obtained. The local linear estimator for link function achieves optimal convergence rate. By using the bias-correction and inverse selection probability weighted methods, a class of empirical likelihood ratios is proposed such that each of our class of ratios is asymptotically chi-squared. A simulation study indicates that the proposed methods are comparable in terms of coverage probabilities and average lengths (areas) of confidence intervals (regions). An example of a real data set is illustrated.