Inference for single-index quantile regression models with profile optimization
提出伪剖面似然方法估计和检验单指标分位数回归模型，证明了系数估计的渐近正态性和非参数函数的最优收敛速度，并利用惩罚过程同时进行模型选择和估计。
Single index models offer greater flexibility in data analysis than linear models but retain some of the desirable properties such as the interpretability of the coefficients. We consider a pseudo-profile likelihood approach to estimation and testing for single-index quantile regression models. We establish the asymptotic normality of the index coefficient estimator as well as the optimal convergence rate of the nonparametric function estimation. Moreover, we propose a score test for the index coefficient based on the gradient of the pseudo-profile likelihood, and employ a penalized procedure to perform consistent model selection and model estimation simultaneously. We also use Monte Carlo studies to support our asymptotic results, and use an empirical example to illustrate the proposed method.