Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis
Ana-Maria Staicu, Yingxing Li, Ciprian M. Crainiceanu, David Ruppert
Scandinavian Journal of Statistics
#002307 20160221 ()
This 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 as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized splines; and (2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo-likelihood ratio test is proposed, and its asymptotic distribution is derived. The size and power properties of the test are confirmed 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 ı-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.
Keywords: functional data, longitudinal data, pseudo-likelihood, sleep health heart study, two-sample problem

Download full text