On average derivative quantile regression
On average derivative quantile regression
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DOI：
10.1214/aos/1031833670
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发表时间：
1997-04
影响因子：
4.5
通讯作者：
P. Chaudhuri;K. Doksum;A. Samarov
中科院分区：
文献类型：
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作者：
P. Chaudhuri;K. Doksum;A. Samarov
对于固定的α ∈（0，1），分位数回归函数给出响应变量Y的条件分布中的第α分位数θ α（x），给定协变量向量的值X = x。它不仅可以用来衡量协变量在总体中心的影响，而且可以用来衡量协变量在上尾和下尾的影响。总结X和Y之间的分位数特定关系的关键特征的泛函是分位数函数θ α（x）的偏导数向量的加权期望值的向量β α。在非参数设置中，β α可以被视为分位数特定非参数回归系数的向量。在生存分析模型中（例如，考克斯的比例风险模型、比例优势率模型、加速失效时间模型），在回归分析中使用的单调变换模型中，β α给出了模型参数部分中参数向量的方向。β α也可以用来估计计量经济学中流行的半参数单指数模型中参数向量的方向。证明了在适当的正则性条件下，利用Chaudhuri（1991 a）的局部多项式分位数估计得到的β α的估计是n1/2相合的，渐近正态的，渐近方差等于泛函β α的影响函数的方差.本文讨论了β α的估计如何用于模型诊断和构造一般单指标模型中的连接函数估计。
For fixed α ∈ (0,1), the quantile regression function gives the αth quantile θ α (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 β α of weighted expected values of the vector of partial derivatives of the quantile function θ α (x). In a nonparametric setting, β α 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, β α gives the direction of the parameter vector in the parametric part of the model. β α 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 β α 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 β α . We discuss how the estimate of β α can be used for model diagnostics and in the construction of a link function estimate in general single index models.