@article{TEXTUAL,
      recid = {8441},
      author = {Zhang, Huiming and Lei, Xiaoyu},
      title = {Growing-dimensional partially functional linear models:  Non-asymptotic optimal prediction error},
      journal = {Physica Scripta},
      address = {2023-08-09},
      number = {TEXTUAL},
      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.},
      url = {http://knowledge.uchicago.edu/record/8441},
}