{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T14:13:44Z","timestamp":1654870424602},"reference-count":56,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T00:00:00Z","timestamp":1622678400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p>The weighted average quantile derivative (AQD) 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: a known function chosen by researchers and the density function of the covariates that is parallel to the average mean derivative in Powell, Stock, and Stoker (1989, <jats:italic>Econometrica<\/jats:italic> 57, 1403\u20131430). The AQD summarizes the marginal response of the covariates on the CQF and defines a nonparametric quantile regression coefficient. In semiparametric single-index and partially linear models, the AQD identifies the coefficients up to scale. In nonparametric nonseparable structural models, the AQD conveys an average structural effect under certain independence assumptions. Including a stochastic trimming function, the proposed two-step estimator is root-<jats:italic>n<\/jats:italic>-consistent for the AQD defined by the <jats:italic>entire<\/jats:italic> support of the covariates. To facilitate tractable asymptotic analysis, 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 <jats:italic>expanding<\/jats:italic> compact set and over the quantile levels. The weak convergence to Gaussian processes applies to the differentiable nonlinear functionals of the quantile processes.<\/jats:p>","DOI":"10.1017\/s0266466621000232","type":"journal-article","created":{"date-parts":[[2021,6,3]],"date-time":"2021-06-03T12:22:14Z","timestamp":1622722934000},"page":"497-535","source":"Crossref","is-referenced-by-count":0,"title":["NONPARAMETRIC WEIGHTED AVERAGE QUANTILE 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