On average derivative quantile regression

• 成果类型: Article
• 署名作者: Chaudhuri, P; Doksum, K; Samarov, A
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Kolkata; University of California System; University of California Berkeley; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 715-744
• 关键词: binary response models; nonparametric-estimation; conditional quantile; index models; kernel; transformations

摘要

For fixed alpha epsilon (0, 1), the quantile regression function gives the alpha th quantile theta(alpha)(x) in the conditional distribution of a response variable Y given the value X = x of a vector of covariates. It can be used to measure the effect of covariates not only in the center of a population, but also in the upper and lower tails. A functional that summarizes key features of the quantile specific relationship between X and Y is the vector beta(alpha) of weighted expected values of the vector of partial derivatives of the quantile function theta(alpha)(x). In a nonparametric setting, beta(alpha) can be regarded as a vector of quantile specific nonparametric regression coefficients. In survival analysis models (e.g., Cox's proportional hazard model, proportional odds rate model, accelerated failure time model) and in monotone transformation models used in regression analysis, beta(alpha) gives the direction of the parameter vector in the parametric part of the model. beta(alpha) can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics. We show that, under suitable regularity conditions, the estimate of beta(alpha) obtained by using the locally polynomial quantile estimate of Chaudhuri (1991a) is n(1/2)-consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional beta(alpha). We discuss how the estimate of beta(alpha) can be used for model diagnostics and in the construction of a link function estimate in general single index models.