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Functional Partial Least-Squares: Optimal Rates and Adaptation (2402.11134v1)

Published 16 Feb 2024 in math.ST, econ.EM, stat.CO, stat.ME, stat.ML, and stat.TH

Abstract: We consider the functional linear regression model with a scalar response and a Hilbert space-valued predictor, a well-known ill-posed inverse problem. We propose a new formulation of the functional partial least-squares (PLS) estimator related to the conjugate gradient method. We shall show that the estimator achieves the (nearly) optimal convergence rate on a class of ellipsoids and we introduce an early stopping rule which adapts to the unknown degree of ill-posedness. Some theoretical and simulation comparison between the estimator and the principal component regression estimator is provided.

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