Locally sparse estimation for simultaneous functional quantile regression

TL;DR

This paper introduces a novel simultaneous functional quantile regression model with locally sparse bivariate slope functions, improving interpretability and efficiency in analyzing how functional predictors influence responses across multiple quantiles.

Contribution

It proposes a new FQR model with locally sparse slopes that vary by quantile, enabling simultaneous estimation and enhanced interpretability over traditional methods.

Findings

The method accurately identifies non-impact periods of temperature on soybean yield.

Simulation studies show the approach outperforms standard quantile regression techniques.

Application to soybean data reveals key temperature periods affecting yield.

Abstract

Motivated by the study of how daily temperature affects soybean yield, this article proposes a simultaneous functional quantile regression (FQR) model featuring a locally sparse bivariate slope function indexed by both quantile and time and linked to a functional predictor. The slope function's local sparsity means it holds non-zero values only in certain segments of its domain, remaining zero elsewhere. These zero-slope regions, which vary by quantile, indicate times when the functional predictor has no discernible impact on the response variable. This feature boosts the model's interpretability. Unlike traditional FQR models, which fit one quantile at a time and have several limitations, our proposed method can handle a spectrum of quantiles simultaneously. We tested the new approach through simulation studies, demonstrating its clear advantages over standard techniques. To validate its practical use, we applied the method to soybean yield data, pinpointing the time periods when daily temperature doesn't affect yield. This insight could be crucial for agricultural planning and crop management.