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Linear Regression Using Hilbert-Space-Valued Covariates with Unknown Reproducing Kernel (2504.16780v1)
Published 23 Apr 2025 in math.ST, stat.ME, and stat.TH
Abstract: We present a new method of linear regression based on principal components using Hilbert-space-valued covariates with unknown reproducing kernels. We develop a computationally efficient approach to estimation and derive asymptotic theory for the regression parameter estimates under mild assumptions. We demonstrate the approach in simulation studies as well as in data analysis using two-dimensional brain images as predictors.
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