Smoothed Quantile Regression with Large-Scale Inference.

ABSTRACT: Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. This paper focuses on statistical inference for quantile regression in the "increasing dimension" regime. We provide a comprehensive analysis of a convolution smoothed approach that achieves adequate approximation to computation and inference for quantile regression. This method, which we refer to as conquer, turns the non-differentiable check function into a twice-differentiable, convex and locally strongly convex surrogate, which admits fast and scalable gradient-based algorithms to perform optimization, and multiplier bootstrap for statistical inference. Theoretically, we establish explicit non-asymptotic bounds on es

SUBMITTER: He X 

PROVIDER: S-EPMC9912996 | biostudies-literature | 2023 Feb

REPOSITORIES: biostudies-literature