Nonparametric inference methods on the mean difference between two correlated Functional processes are proposed. We compare methods that: 1) incorporate different levels of smoothing of the mean and covariance; 2) preserve the sampling design; and 3) use parametric and nonparametric estimation of the mean functions. We apply our method to estimating the mean difference between average normalized δ-power of sleep electroencephalograms for 51 subjects with severe sleep apnea and 51 matched controls in the first 4 hours after sleep onset. Data are obtained from the Sleep Heart Health Study (SHHS), the largest community cohort study of sleep. While methods are applied to a single case study, they can be applied to a large number of studies that have correlated functional data.
Crainiceanu, Ciprian M.; Staicu, Ana-Maria; Ray, Shubankar; and Punjabi, Naresh, "BOOTSTRAP-BASED INFERENCE ON THE DIFFERENCE IN THE MEANS OF TWO CORRELATED FUNCTIONAL PROCESSES" (March 2012). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 225.