In this talk I introduce a general inferential framework for testing hypotheses about the population mean function against semiparametric alternatives, in the context of dependent data such as functional data. The methodology is based on a pseudo likelihood approach, by treating the noise process's covariance function as an infinite-dimensional nuisance parameter and replacing it by a consistent estimator. Theoretical results for the asymptotic distribution of the pseudo likelihood ratio test are provided, and their performance is investigated numerically. The proposed methods are applied to a Sleep Health Heart Study, where the interest is testing the equality between the average normalized d-power of sleep electroencephalograms of subjects with severe sleep apnea and of matched controls.
Dept of Biostatistics
biostats [at] columbia [dot] edu