Locally sparse estimation for simultaneous functional quantile regression

2026-02-02

AI Summary

This study addresses the limitations of traditional functional quantile regression models, which fit quantiles pointwise and thus fail to simultaneously capture the local effects of functional predictors across multiple quantile levels or automatically identify time intervals with no effect. To overcome these challenges, we propose a simultaneous functional quantile regression method that introduces a bivariate slope function endowed with local sparsity in both the time and quantile dimensions. This approach enables joint modeling across multiple quantiles and automatically detects time intervals where the functional predictor has no significant impact on the response. By integrating regularization techniques, our method effectively estimates the underlying spatiotemporal sparse structure. Simulation studies demonstrate its superior performance over existing methods, and an application to soybean yield data successfully identifies critical periods during which daily temperature exerts no influence on yield, offering valuable insights for agricultural decision-making.

Technology Category

• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• functional quantile regression
• local sparsity
• simultaneous estimation
• functional predictor
• interpretability

Innovation

• simultaneous functional quantile regression
• locally sparse slope function
• functional data analysis
• quantile-varying sparsity
• agricultural application