B1874
Title: Functional linear regression: Linear hypothesis testing with functional response
Authors: Dengdeng Yu - UTSA (United States) [presenting]
Abstract: Hypothesis testing is a crucial aspect of functional data analysis, allowing researchers to make inferential decisions based on samples of functional data. The inherent infinite dimensionality of functional data makes conventional hypothesis testing methods difficult to apply. To address this issue, a common practice is to project functional data into a lower-dimensional space prior to testing. Nonetheless, the selection of this projection space can influence the test's validity and power. A novel hypothesis testing procedure is proposed that establishes an optimal projection space. In this space, the original and projected hypotheses are equivalent, achieving optimal test power. The theoretical properties of the proposed test are systematically investigated. To assess the performance of the proposed test, extensive numerical analyses are conducted. The results demonstrate the superiority of the proposed projection test for functional linear hypotheses in the function-on-scalar regression linear model.
