Conditional quantile processes based on series or many regressors
Name
1105.6154.pdf
Description
Accepted version
Size
1.8 MB
Format
Adobe PDF
Checksum (MD5)
3ea6d81ec96c89c63dc7f81f7d3758e1
Author(s)
Belloni, Alexandre
Chernozhukov, Victor V
Chetverikov, Denis
Fernández-Val, Iván
Date Issued
August 2019
Journal
Journal of Econometrics
Publisher
Elsevier
Citation
Belloni, Alexandre et al. "Conditional quantile processes based on series or many regressors." Journal of Econometrics 213 (November 2019): 4-29 © 2019 Elsevier
Version
Original manuscript
Abstract
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a linear combination of series terms with quantile-specific coefficients and estimate the function-valued coefficients from the data. We develop large sample theory for the QR-series coefficient process, namely we obtain uniform strong approximations to the QR-series coefficient process by conditionally pivotal and Gaussian processes. Based on these two strong approximations, or couplings, we develop four resampling methods (pivotal, gradient bootstrap, Gaussian, and weighted bootstrap) that can be used for inference on the entire QR-series coefficient function. We apply these results to obtain estimation and inference methods for linear functionals of the conditional quantile function, such as the conditional quantile function itself, its partial derivatives, average partial derivatives, and conditional average partial derivatives. Specifically, we obtain uniform rates of convergence and show how to use the four resampling methods mentioned above for inference on the functionals. All of the above results are for function-valued parameters, holding uniformly in both the quantile index and the covariate value, and covering the pointwise case as a by-product. We demonstrate the practical utility of these results with an empirical example, where we estimate the price elasticity function and test the Slutsky condition of the individual demand for gasoline, as indexed by the individual unobserved propensity for gasoline consumption. Keywords: quantile regression; series; strong approximation; coupling; bootstrap; uniform inference; quantile process
MIT Department
Massachusetts Institute of Technology. Department of Economics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jeconom.2019.04.003
