A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION
A SINGLE-INDEX QUANTILE REGRESSION MODEL AND ITS ESTIMATION
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DOI：
10.1017/s0266466611000788
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发表时间：
2012-03
影响因子：
0.8
通讯作者：
Efang Kong;Yingcun Xia
中科院分区：
文献类型：
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作者：
Efang Kong;Yingcun Xia
具有单指标结构的模型是条件均值或条件方差的许多现有流行的半参数方法之一。本文重点研究了条件分位数的单指标模型。我们提出了一个自适应估计过程和迭代算法，在温和的正则性条件下，证明了收敛概率为1。单指标参数向量的估计是根-n相容的，渐近正态的，并且基于模拟研究，比Chaudhuri，Doksum和Samarov（1997，Annals of Statistics 19，760-777）中的平均导数方法更有效。连结函数的估计量以通常的速度收敛于一元函数的非参数估计。作为一个实证研究，我们应用单指数分位数回归模型的波士顿住房数据。通过考虑不同水平的分位数，我们探讨了社会或环境性质的协变量如何对住房市场的低端、中端和高端人群产生不同的影响。
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.