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Title: Nonparametric weighted average quantile derivative Authors:  Ying-Ying Lee - University of California, Irvine (United States) [presenting]
Abstract: The aim is to estimate the weighted Average Quantile Derivative (AQD), that is, the expected value of the partial derivative of the conditional quantile function (CQF) weighted by a function of the covariates. We consider two weighting functions: (i) a known function chosen by re- searchers; (ii) an estimated density function of the covariates, parallel to a previous density-weighted average mean derivative. The AQD summarizes the average marginal response of the covariates on the CQF and defines a nonparametric quantile regression coefficient. In semi-parametric single-index and partial linear models, the AQD identifies the coefficients up to scale. In nonparametric nonseparable structural models, the AQD conveys an average structural effect. We interpret and estimate the AQD by a weighted average CQF. Including a stochastic trimming function, the proposed two-step estimator is root-n-consistent for the AQD defined on the entire support of the covariates. A key preliminary result is a new Bahadur- type linear representation of the generalized inverse kernel-based CQF estimator uniformly over the covariates in an expanding compact set and over the quantile levels. Our asymptotic normality results can be extended to the Hadamard-differentiable functionals of the conditional or average quantile processes, which can be nonlinear functionals of the distributions.