Nonparametric quantile regression for spatio-temporal processes

TL;DR

This paper introduces a novel nonparametric quantile regression method tailored for high-dimensional spatio-temporal data, addressing computational challenges and providing robust inference tools with theoretical and empirical validation.

Contribution

It develops a new approach that handles ultrahigh-dimensional predictors in spatio-temporal settings, with theoretical guarantees and practical inference procedures.

Findings

Effective in ultrahigh-dimensional regimes

Provides simultaneous confidence intervals and hypothesis tests

Validated through simulations and real-world electricity demand data

Abstract

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational challenges that constitute known hindrances to existing nonparametric quantile regression methods when the number of predictors is much larger than the available sample size. We investigate conditions under which estimation is feasible and of good overall quality and obtain sharp approximations that we employ to devising statistical inference methodology. These include simultaneous confidence intervals and tests of hypotheses, whose asymptotics is borne by a non-trivial functional central limit theorem tailored to martingale differences. Additionally, we provide finite-sample results through various simulations which, accompanied by an illustrative application to real-worldesque data (on electricity demand), offer guarantees on the performance of the proposed methodology.