Functional Partial Least-Squares: Adaptive Estimation and Inference

• 成果类型: Article; Early Access
• 署名作者: Babii, Andrii; Carrasco, Marine; Tsafack, Idriss
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Universite de Montreal
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2582874
• 发表日期: 2026-01-08
• 关键词: Climate science; Functional linear regression; Functional partial least-squares; inference; Rate-optimal and adaptive estimation; PRINCIPAL COMPONENT REGRESSION; KERNEL CONJUGATE-GRADIENT; convergence-rates; PLS; methodology; prediction

摘要

We study the linear regression model with a scalar response and a functional predictor, a canonical example of an ill-posed inverse problem. We show that the functional partial least-squares (PLS) estimator achieves convergence rates that are nearly minimax-optimal over a class of ellipsoids and propose an adaptive early-stopping procedure for selecting the number of PLS components. In addition, we develop a new test that detects parametric local alternatives. The test can be inverted to construct confidence sets for the functional slope parameter. Simulation results show that the estimator performs favorably relative to several existing methods, and that the proposed test has good power. We apply our methodology to evaluate the nonlinear effects of temperature on corn and soybean yields. We provide a Python software library, fpls, implementing our method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.