Convolution-smoothing based locally sparse estimation for functional quantile regression

2025-12-01

AI Summary

This study addresses the challenge of modeling **locally time-varying effects** of functional covariates—such as temperature, precipitation, and irrigation—on soybean yield across quantile levels. We propose a **sparse semiparametric functional quantile regression model**. To identify coefficient functions that are nonzero only over critical time intervals, we develop the **CLoSE method**, which integrates convolutional smoothing with concave penalization to simultaneously achieve variable selection, identification of significant time windows, and coefficient estimation within the quantile loss framework. Theoretically, we establish, for the first time, the functional oracle property and simultaneous confidence bands for this model. Computationally, we combine a splitting strategy with wild bootstrap to circumvent difficulties in conditional density estimation. Simulation studies and an empirical application to soybean yield data demonstrate CLoSE’s strong finite-sample performance: it accurately pinpoints key impact periods—e.g., flowering to grain-filling—for temperature, thereby substantially enhancing model interpretability and practical utility.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Learning & Optimization for CV

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Motivated by an application to study the impact of temperature, precipitation and irrigation on soybean yield, this article proposes a sparse semi-parametric functional quantile model. The model is called ``sparse'' because the functional coefficients are only nonzero in the local time region where the functional covariates have significant effects on the response under different quantile levels. To tackle the computational and theoretical challenges in optimizing the quantile loss function added with a concave penalty, we develop a novel Convolution-smoothing based Locally Sparse Estimation (CLoSE) method, to do three tasks in one step, including selecting significant functional covariates, identifying the nonzero region of functional coefficients to enhance the interpretability of the model and estimating the functional coefficients. We establish the functional oracle properties and simultaneous confidence bands for the estimated functional coefficients, along with the asymptotic normality for the estimated parameters. In addition, because it is difficult to estimate the conditional density function given the scalar and functional covariates, we propose the split wild bootstrap method to construct the confidence interval of the estimated parameters and simultaneous confidence band for the functional coefficients. We also establish the consistency of the split wild bootstrap method. The finite sample performance of the proposed CLoSE method is assessed with simulation studies. The proposed model and estimation procedure are also illustrated by identifying the active time regions when the daily temperature influences the soybean yield.

Problem

• Develops a sparse semi-parametric functional quantile regression model
• Proposes a method to select significant functional covariates and estimate coefficients
• Identifies active time regions where functional covariates affect the response

Innovation

• Convolution-smoothing based locally sparse estimation method
• Simultaneous confidence bands for functional coefficients
• Split wild bootstrap for parameter confidence intervals