Significance tests for functional data with complex dependence structure

• Published in: Journal of statistical planning and inference Vol. 156; pp. 1 - 13
• Main Authors: Staicu, Ana-Maria, Lahiri, Soumen N., Carroll, Raymond J.
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.01.2015
• Subjects: Block bootstrap; Functional data; Group mean testing; Hierarchical modeling; Significance tests; Spatially correlated curves; Significance tests; Spatially correlated curves; Block bootstrap; Functional data; Group mean testing; Hierarchical modeling
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2014.08.006

We propose an L2-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups–clusters or subjects–units, where the unit-level profiles are spatially correlated within the cluster, and the cluster-level data are independent. Orthogonal series expansions are used to approximate the group mean functions and the test statistic is estimated using the basis coefficients. The asymptotic null distribution of the test statistic is developed, under mild regularity conditions. To our knowledge this is the first work that studies hypothesis testing, when data have such complex multilevel functional and spatial structure. Two small-sample alternatives, including a novel block bootstrap for functional data, are proposed, and their performance is examined in simulation studies. The paper concludes with an illustration of a motivating experiment. •We propose significance tests for group mean functions when the data are complex correlated curves.•Asymptotic null distribution of the testing procedures is developed.•Approximations to the null distribution are proposed including: single level bootstrap, and novel nested bootstrap.•The procedures are illustrated through simulations and data application.