Hypothesis Testing of Functional Data with Applications to Longitudinal Studies

• Activity Number: 86
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): Kun Nie*+ and Xiaowei Yang and Gang Li and Steven Shoptaw
• Companies: BayesSoft, Inc. and BayesSoft, Inc. and University of California, Los Angeles and BayesSoft, Inc.
• Keywords: longitudinal study ; functional linear regression ; adaptive Neyman test ; thresholding test ; Fourier transform ; wavelets transform

Abstract

Longitudinal studies in certain fields contain large number of repeated measures on each subject. The high dimensionality and temporal correlations of data erode the power of traditional testing methods seriously. Within the frame of functional linear regression models where the observations of the same subject are viewed as a sample from a functional space, we develop a new strategy for hypothesis testing problems. First, we perform the Fourier/wavelet transforms to each set of observation, which serve to reduce temporal correlations and compress useful signals into a few components; second, linear regressions are applied in the Fourier/wavelet domain; then the significance of the regression coefficients are tested based on the adaptive Neyman or thresholding test statistics. The simulation results showed that both the adaptive Neyman and thresholding approaches significantly enhance sensitivities over traditional methods such as pointwise regression with Bonferonni corrections or univariate analysis where each set of observations is collapsed into a composite score. The methods are illustrated with an example of a smoking cessation study.