Back To Index Previous Article Next Article Full Text

Statistica Sinica 31 (2021), 1101-1123

HYPOTHESIS TESTING IN
LARGE-SCALE FUNCTIONAL LINEAR REGRESSION

Kaijie Xue and Fang Yao

Nankai University and Peking University

Abstract: We explore large-scale functional linear regression in which the scalar response is associated with a potentially ultrahigh number of functional predictors, leading to a more challenging model framework than the classical case. We establish a rigorous procedure for testing a general hypothesis on an arbitrary subset of regression coefficient functions. Specifically, we exploit the techniques developed for post-regularization inferences, and propose a new test for the aforementioned regression based on a decorrelated score function that separates the primary and nuisance parameters in functional spaces. We also devise the corresponding decorrelated Wald and likelihood ratio tests, and establish the exact equivalence among these three tests for the model under consideration. The proposed test is shown to be uniformly convergent to the prescribed significance. We show its finite-sample performance using simulation studies and a data set from the Human Connectome Project that identifies brain regions associated with emotional tasks.

Key words and phrases: Decorrelated score, functional data, functional linear regression, high dimensions, multiplier bootstrap.

Back To Index Previous Article Next Article Full Text