Inferences in a Censored Single-index Model with Empirical Likelihood
删失数据下单指标模型的经验似然推断

Empirical likelihood method for single-index models with randomly censored data is investigated. An estimated empirical likelihood for the parameters by using a synthetic data approach is developed. An adjusted empirical log-likelihood ratio function is proven to be asymptotically standard chi-squared, and the corresponding confidence regions of the parameters are then constructed. Furthermore, since the index is of norm 1, this constraint is used to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study indicates that compared with a normal approximation method, the proposed method works better in terms of coverage probabilities and areas of confidence regions.