General Linear Hypothesis Testing in Ill-conditioned Functional Response Model

Accepted - May 2025

Abstract

The paper focuses on inference in the ill-conditioned functional response model, a type of regression model commonly used in functional data analysis. In this model, the response, which is a functional variable, is explained using several independent scalar variables. In certain practical scenarios, the design matrix may lack full rank, leading to an ill-conditioned model. This makes inference more challenging compared to standard models. To address this issue, we propose new test statistics for verifying general linear hypotheses. These statistics aggregate F-type pointwise test statistics using either integration or the supremum. A key advantage of our test statistics is their scale invariance, in contrast to existing ones. To construct the proposed tests, we employ various bootstrap techniques, which do not need any distribution assumptions and demonstrate good finite-sample performance. We evaluate the effectiveness of the new tests through both simulation studies and an application to real-world data. Our results indicate that the new test procedures maintain appropriate control of the type I error rate and generally exhibit greater statistical power compared to existing methods.