Abstract

In this work, we extend the classical generalized functional linear model to a

large-scale generalized functional linear model to handle a variety of complex situations

where the response (possibly discrete) can be nonlinearly linked to an ultra-high number

of functional predictors. Unlike most existing requirements on functional data, we don’t

need to impose any conditions regarding eigenvalue-decay or square-integrability on those

functional predictors, resulting in a more flexible but challenging model framework. Based

on a penalized model estimator, we develop a general inferential method to assess the significance of an arbitrary group of regression curves. Concretely, a pseudo score function is

adopted to construct the associated confidence region for the regression curves of interest.

Notably, the proposed test is justified uniformly convergent to nominal level, without any

demand on estimation consistency of the regression curves. Finally, numerical studies are

carried out to show the empirical performance of the proposed test.

Information

Preprint No.SS-2023-0356
Manuscript IDSS-2023-0356
Complete AuthorsKaijie Xue, Riquan Zhang
Corresponding AuthorsRiquan Zhang
Emailszhangriquan@163.com

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (12371268, 12371272), the Youth Project of

Shanghai Eastern Talent Program (QNJY2024152), and the Basic Research Project

of Shanghai Science and Technology Commission (22JC1400800).

Supplementary Materials

The auxiliary lemmas with their proofs, and the proofs of the main theorems

are delegated to an online Supplementary Material for space economy.

Supplementary materials are available for download.