A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION
提出一种单指标分位数回归模型的自适应估计方法和迭代算法，该算法几乎必然收敛，估计量具有根号n一致性和渐近正态性，且比平均导数法更有效。通过波士顿房价数据展示了不同分位点下协变量的异质效应。
Models with single-index structures are among the many existing popular semiparametric approaches for either the conditional mean or the conditional variance. This paper focuses on a single-index model for the conditional quantile. We propose an adaptive estimation procedure and an iterative algorithm which, under mild regularity conditions, is proved to converge with probability 1. The resulted estimator of the single-index parametric vector is root- n consistent, asymptotically normal, and based on simulation study, is more efficient than the average derivative method in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). The estimator of the link function converges at the usual rate for nonparametric estimation of a univariate function. As an empirical study, we apply the single-index quantile regression model to Boston housing data. By considering different levels of quantile, we explore how the covariates, of either social or environmental nature, could have different effects on individuals targeting the low, the median, and the high end of the housing market.