Biostatistics Seminar: Yu-Ru Su
DATE: Tuesday, June 3rd, 2014
TIME: 4:10pm (refreshments at 3:30pm, MSB 4110)
LOCATION: Mathematical Sciences Building 1147
SPEAKER: Yu-Ru Su, Fred Hutchison Cancer Research Center
TITLE: Hypothesis testing for functional linear models with scalar responses
ABSTRACT: In the last decade, functional data arise frequently in many biomedical studies, where it is often of interest to investigate the dynamic association of functional predictors with a scalar response. While functional linear models (FLM) are widely used to answer these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to test the functional effects is through dimension reduction, such as functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not well studied. We investigate the power performance of the Wald-type test with varying thresholds in selecting the number of PCs for the functional covariates, and find that the thresholds have a great impact on the performance of the test. To circumvent the issue, a new method of ordering and selecting principal components is proposed to construct test statistics. The method takes into account both the association with the response and the variation along each eigenfunction. We explore both the theoretical and numerical properties of the proposed test. Our simulation results show that the proposed test is more robust than the existing test while being more powerful than the existing method under some scenarios. We apply the proposed method to the cerebral white matter tracts data obtained from a diffusion tensor imaging tractography study.