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• W4385319305 abstract "Abstract Under the reproducing kernel Hilbert spaces (RKHS), we focus on the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate part allows a divergent number of parameters. From the non-asymptotic point of view, we study the rate-optimal upper and lower bounds of the prediction error. An exact upper bound for the excess prediction risk is shown in a non-asymptotic form under a more general assumption known as the effective dimension to the model, by which we also show the prediction consistency when the number of multivariate covariates p slightly increases with the sample size n . Our new finding implies a trade-off between the number of non-functional predictors and the effective dimension of the kernel principal components to ensure prediction consistency in the increasing-dimensional setting. The analysis in our proof hinges on the spectral condition of the sandwich operator of the covariance operator and the reproducing kernel, and on sub-Gaussian and Berstein concentration inequalities for the random elements in Hilbert space. Finally, we derive the non-asymptotic minimax lower bound under the regularity assumption of the Kullback-Leibler divergence of the models." @default.
• W4385319305 created "2023-07-28" @default.
• W4385319305 creator A5027899074 @default.
• W4385319305 creator A5046908163 @default.
• W4385319305 date "2023-08-09" @default.
• W4385319305 modified "2023-10-17" @default.
• W4385319305 title "Growing-dimensional Partially Functional Linear Models: Non-asymptotic Optimal Prediction Error" @default.
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• W4385319305 doi "https://doi.org/10.1088/1402-4896/aceac0" @default.
• W4385319305 hasPublicationYear "2023" @default.
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