Optimal subsampling for functional quantile regression

TL;DR

This paper develops optimal subsampling strategies for functional quantile regression, improving computational efficiency and accuracy in large datasets by deriving asymptotic properties and proposing practical sampling probabilities.

Contribution

It introduces the first asymptotic analysis for subsampling in functional quantile regression and proposes easy-to-implement optimal sampling probabilities.

Findings

Proposed methods outperform uniform sampling in simulations.

Methods approximate full data results with less computation.

Modified probabilities are easier to implement in practice.

Abstract

Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator is first derived. Then, we obtain the optimal subsampling probabilities based on the A-optimality criterion. Furthermore, the modified subsampling probabilities without estimating the densities of the response variables given the covariates are also proposed, which are easier to implement in practise. Numerical experiments on synthetic and real data show that the proposed methods always outperform the one with uniform sampling and can approximate the results based on full data well with less computational efforts.