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 hypotheses that the mean of a functional process is parametric against a general alternative modeled by penalized splines; and 2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or di er 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 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 -power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.
Some Key Words: functional data, longitudinal data, pseudo likelihood, sleep health
heart study, two sample problem.
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