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Detecting and estimating epidemic changes in dependent functional data

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Aston, John A. D. and Kirch, Claudia (2011) Detecting and estimating epidemic changes in dependent functional data. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2011 (No.7).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

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

Official Date:

2011

Dates:

Date	Event
2011	Published

Volume:

Vol.2011

Number:

No.7

Number of Pages:

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Not Peer Reviewed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.