Functional Partial Least-Squares: Optimal Rates and Adaptation

• URL: http://arxiv.org/abs/2402.11134v1
• Date: Fri, 16 Feb 2024 23:47:47 GMT
• Title: Functional Partial Least-Squares: Optimal Rates and Adaptation
• Authors: Andrii Babii and Marine Carrasco and Idriss Tsafack
• Abstract summary: We propose a new formulation of the functional partial least-squares (PLS) estimator related to the conjugate gradient method. We show that the estimator achieves the (nearly) optimal convergence rate on a class of ellipsoids.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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