Aston, John A. D. and Kirch, Claudia (2011) Detecting and estimating epidemic changes in dependent functional data. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

Preview

PDF WRAP_aston_11-07w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (544Kb)

Abstract

Change point detection in sequences of functional data is examined where the functional observations are dependent. Of particular interest is the case where the change point is an epidemic change (a change occurs and then the observations return to baseline at a later time). The theoretical properties for various tests for at most one change and epidemic changes are derived with a special focus on power analysis. Estimators of the change point location are derived from the test statistics and theoretical properties investigated.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Change-point problems
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.7
Number of Pages:	21
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Stifterverband für die Deutsche Wissenschaft, Claussen-Simon-trust, Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/H016856/1 (EPSRC)
References:	[1] Aston, J. A. D. and Kirch, C. Estimation of the distribution of change-points with application to fMRI data Technical Report, 2011. [2] Aue, A., Gabrys, R., Horvath, L., and Kokoszka, P. Estimation of a change-point in the mean function of functional data. J. Multivariate Anal., 100:2254{2269, 2009. [3] Berkes, I., Gabrys, R., Horvath, L., and Kokoszka, P. Detecting changes in the mean of functional observations. J. R. Stat. Soc. Ser. B Stat. Methodol., 71:927{946, 2009. [4] Bosq, D. Linear Processes in Function Spaces. Springer, 2000. [5] Dehling, H. Limit theorems for sums of weakly dependent Banach space valued random variables. Z. Wahrsch. verw. Geb., 63:393{432, 1983. [6] Dehling, H. and Philipp, W. Almost sure invariance principles for weakly dependent vectorvalued random variables. Ann. Probab., 10:689{701, 1982. [7] Dudley, R. M. and Philipp, W. Invariance principles for sums of Banach space valued random elements and empirical processes. Z. Wahrsch. verw. Geb., 62:509{552, 1983. [8] Ferraty, F. and Vieu, P. Nonparametric Functional Data Analysis: Theory and Practice. Springer, New York, 2006. [9] Gohberg, I., Goldberg, S., and Kaashoek, M. A. Basic classes of linear operators. Birkhauser, Boston, 2003. [10] Hormann, S. and Kokoszka, P. Weakly dependent functional data. Ann. Statist., 38:1845{1884, 2010. [11] Horvath, L. and Kokoszka, P. Inference for Functional Data with Applications. Book in preparation. 2011. [12] Horvath, L., Kokoszka, P., and Steinebach, J. Testing for changes in multivariate dependent observations with an application to temperature changes. J. Multivariate Anal., 68:96{119, 1999. [13] Huskova, M. and Kirch, C. A note on studentized confidence intervals in change-point analysis. Comput. Statist., 25:269{289, 2010. [14] Kokoszka, P., and Leipus, R. Change-point in the mean of dependent observations. Statist. Probab. Lett., 40:385{393, 1998. [15] Kuelbs, J., and Philipp, W. Almost sure invariance principles for partial sums of mixing b-valued random variables. Ann. Probab., 8:1003{1036, 1980. [16] Politis, D.N. Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices. To appear in Econometric Theory. Preprint: Department of Economics, UCSD, Paper 2005-03R, http://repositories.cdlib.org/ucsdecon/2005-03R. [17] Ramsay, J. O. and Silverman, B. W. Functional Data Analysis. Springer, Berlin, 2nd edition, 2005. [18] Ranga Rao, R. Relation between weak and uniform convergence of measures with applications. Ann. Math. Statist., 33:659{680, 1962. [19] Ser ing, R.J. Convergence properties of Sn under moment restrictions. Ann. Math. Statist., 41:1235{1248, 1970.
URI:	http://wrap.warwick.ac.uk/id/eprint/34877

Request changes to a record

Actions (login required)

View Item