Pseudo-Likelihood Ratio Tests for Longitudinal and Functional Data Analysis

• Activity Number: 7
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Ana-Maria Staicu*+ and Yingxing Li and Ciprian Crainiceanu and David Ruppert
• Companies: North Carolina State University and Wang Yanan Institute for Studies in Economics and The Johns Hopkins University and Cornell University
• Keywords: functional data ; likelihood ratio test ; pseudo likelihood ; Sleep Health Heart Study ; hypotheses testing ; two sample problem

Abstract

The paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are: 1) testing the null hypothesis that the mean of a functional process is parametric against a nonparametric alternative; and 2) testing the null hypothesis that the means of two possibly correlated functional processes are equal. A global pseudo likelihood ratio tests is proposed and its asymptotic distribution is derived. The size and power properties of the test are conrmed in realistic simulation scenarios. Finite sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized delta-power of sleep electroencephalograms of subjects with severe sleep apnea and matched controls.