General linear hypothesis testing in ill-conditioned functional response model

TL;DR

This paper develops new scale-invariant hypothesis tests for ill-conditioned functional response models in functional data analysis, utilizing bootstrap methods and aggregation of pointwise statistics, with demonstrated improved performance.

Contribution

It introduces novel scale-invariant test statistics for functional response models and compares their effectiveness using bootstrap methods in simulations and real data.

Findings

New tests are scale-invariant, unlike existing methods.

Bootstrap methods effectively construct the tests.

New tests outperform some existing methods in simulations.

Abstract

The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify linear hypotheses, we develop new test statistics by aggregating pointwise statistics using either integral or supremum. The new tests are scale-invariant, in contrast to the existing ones. To construct tests, we use different bootstrap methods. The performance of the new tests is compared with the performance of known tests through a simulation study and an application to a real data example.