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Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimality

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

Functional data analysis is an important statistical field that treats data as random functions. In practice, the random functions are often not fully observed but instead measured at discrete times. While simpler problems, such as mean and covariance estimation, have been widely studied for discretely observed data, optimal estimation of linear regression for this data type has remained unsolved for over two decades. To tackle this fundamental challenge, we propose a novel approach, referred to as pooling ridge estimation, which combines the advantages of pooling strategy and RKHS-based metho

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