Conditional quantile processes based on series or many regressors

Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov and Ivan Fernandez-Val ()

Journal of Econometrics, 2019, vol. 213, issue 1, 4-29

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.

Keywords: Quantile regression; Series; Strong approximation; Coupling; Bootstrap; Uniform inference; Quantile process (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (32)

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Related works:
Working Paper: Conditional Quantile Processes based on Series or Many Regressors (2018)
Working Paper: Conditional quantile processes based on series or many regressors (2016)
Working Paper: Conditional quantile processes based on series or many regressors (2016)
Working Paper: Conditional quantile processes based on series or many regressors (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:213:y:2019:i:1:p:4-29

DOI: 10.1016/j.jeconom.2019.04.003

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