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 () Views:2277

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.

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Keywords: functional data, longitudinal data, pseudo-likelihood, sleep health heart study, two-sample problem