Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Locally sparse estimation for simultaneous functional quantile regression

Boyi Hu, Jiguo Cao

TL;DR

This work advances simultaneous functional quantile regression by introducing a locally sparse, smoothly estimated bivariate slope $\beta(t,u)$ that links a functional predictor $X(t)$ to conditional quantiles $Q_Y(u|\mathbf{Z},X)$. The slope is approximated with triangulation-based bivariate splines and regularized with a roughness penalty plus a group LASSO to identify inactive time–quantile regions, enabling interpretable, region-specific inference across multiple quantiles. The authors provide theoretical guarantees for the estimator, demonstrate favorable performance in simulations, and apply the method to Kansas soybean yield data, uncovering temporally varying temperature effects across quantiles that inform agricultural planning. Computationally, the approach is built on convex optimization (SOCP via CVXR), and the work discusses monotonicity concerns, suggesting future enhancements for non-crossing quantile constraints. Overall, the method improves interpretability and efficiency in functional quantile analysis, offering a practical tool for environmental and agricultural applications.

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.

Locally sparse estimation for simultaneous functional quantile regression

TL;DR

This work advances simultaneous functional quantile regression by introducing a locally sparse, smoothly estimated bivariate slope that links a functional predictor to conditional quantiles . The slope is approximated with triangulation-based bivariate splines and regularized with a roughness penalty plus a group LASSO to identify inactive time–quantile regions, enabling interpretable, region-specific inference across multiple quantiles. The authors provide theoretical guarantees for the estimator, demonstrate favorable performance in simulations, and apply the method to Kansas soybean yield data, uncovering temporally varying temperature effects across quantiles that inform agricultural planning. Computationally, the approach is built on convex optimization (SOCP via CVXR), and the work discusses monotonicity concerns, suggesting future enhancements for non-crossing quantile constraints. Overall, the method improves interpretability and efficiency in functional quantile analysis, offering a practical tool for environmental and agricultural applications.

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.
Paper Structure (7 sections, 3 theorems, 19 equations, 1 figure)

This paper contains 7 sections, 3 theorems, 19 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Simultaneous Functional Quantile Regression
  3. Locally Sparse Estimation for $\beta(t,u)$
  4. Parameter Tuning
  5. Theoretical Properties
  6. Real Data Analysis
  7. Conclusions and Discussion

Key Result

Theorem 1

Under the assumptions A1-A6, suppose $n_b \sim |\Delta|^{-(d+1)/\nu}$, and $n_u$ is large enough, then except on a set whose probability goes to zero as $n$ goes to infinity.

Figures (1)

  • Figure 1: The Estimated slope function $\beta(t,u)$ for the simultaneous functional quantile regression model \ref{['soybean_model']} based on the Kansas soybean yield data set.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Corollary 1