Significance tests for functional data with complex dependence structure

Handle URI:
http://hdl.handle.net/10754/599370
Title:
Significance tests for functional data with complex dependence structure
Authors:
Staicu, Ana-Maria; Lahiri, Soumen N.; Carroll, Raymond J.
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.
Citation:
Staicu A-M, Lahiri SN, Carroll RJ (2015) Significance tests for functional data with complex dependence structure. Journal of Statistical Planning and Inference 156: 1–13. Available: http://dx.doi.org/10.1016/j.jspi.2014.08.006.
Publisher:
Elsevier BV
Journal:
Journal of Statistical Planning and Inference
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Jan-2015
DOI:
10.1016/j.jspi.2014.08.006
PubMed ID:
26023253
PubMed Central ID:
PMC4443904
Type:
Article
ISSN:
0378-3758
Sponsors:
Staicu's research was supported by US National Science Foundation grant number DMS 1007466. Lahiri's research was partially supported by National Science Foundation grants DMS 0707139 and DMS 1007703. Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). This publication is based in part on the work supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorStaicu, Ana-Mariaen
dc.contributor.authorLahiri, Soumen N.en
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-28T06:05:45Zen
dc.date.available2016-02-28T06:05:45Zen
dc.date.issued2015-01en
dc.identifier.citationStaicu A-M, Lahiri SN, Carroll RJ (2015) Significance tests for functional data with complex dependence structure. Journal of Statistical Planning and Inference 156: 1–13. Available: http://dx.doi.org/10.1016/j.jspi.2014.08.006.en
dc.identifier.issn0378-3758en
dc.identifier.pmid26023253en
dc.identifier.doi10.1016/j.jspi.2014.08.006en
dc.identifier.urihttp://hdl.handle.net/10754/599370en
dc.description.abstractWe 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.en
dc.description.sponsorshipStaicu's research was supported by US National Science Foundation grant number DMS 1007466. Lahiri's research was partially supported by National Science Foundation grants DMS 0707139 and DMS 1007703. Carroll's research was supported by a grant from the National Cancer Institute (R37-CA057030). This publication is based in part on the work supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherElsevier BVen
dc.subjectFunctional Dataen
dc.subjectHierarchical Modelingen
dc.subjectSignificance Testsen
dc.subjectBlock Bootstrapen
dc.subjectGroup Mean Testingen
dc.subjectSpatially Correlated Curvesen
dc.titleSignificance tests for functional data with complex dependence structureen
dc.typeArticleen
dc.identifier.journalJournal of Statistical Planning and Inferenceen
dc.identifier.pmcidPMC4443904en
dc.contributor.institutionDepartment of Statistics, North Carolina State University, United States.en
dc.contributor.institutionDepartment of Statistics, Texas A&M University, United States.en
kaust.grant.numberKUS-CI-016-04en
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