Significance tests for functional data with complex dependence structure

Ana-Maria Staicu, Soumen N. Lahiri, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We propose an L (2)-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.
Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalJournal of Statistical Planning and Inference
Volume156
DOIs
StatePublished - Jan 2015
Externally publishedYes

Fingerprint Dive into the research topics of 'Significance tests for functional data with complex dependence structure'. Together they form a unique fingerprint.

Cite this