Jarušková, Daniela Testing for a change in covariance operator. (English) Zbl 1279.62124 J. Stat. Plann. Inference 143, No. 9, 1500-1511 (2013). Summary: This paper considers a problem of equality of two covariance operators. Using functional principal component analysis, a method for testing equality of \(K\) largest eigenvalues and the corresponding eigenfunctions, together with its generalization to a corresponding change point problem, is suggested. Asymptotic distributions of the test statistics are presented. Cited in 9 Documents MSC: 62H25 Factor analysis and principal components; correspondence analysis 62E20 Asymptotic distribution theory in statistics Keywords:functional data; principal components; two-sample problem; change point problem PDFBibTeX XMLCite \textit{D. Jarušková}, J. Stat. Plann. Inference 143, No. 9, 1500--1511 (2013; Zbl 1279.62124) Full Text: DOI References: [1] Aue, A.; Hörmann, S.; Horváth, L.; Reimherr, M., Break detection in the covariance structure of multivariate time series models, Annals of Statistics, 37, 4046-4087 (2009) · Zbl 1191.62143 [2] Aue, A.; Gabrys, R.; Horváth, L.; Kokoszka, P., Estimation of change-point in the mean function of functional data, Journal of Multivariate Analysis, 100, 2254-2269 (2009) · Zbl 1176.62025 [3] Benko, M.; Härdle, W.; Kneip, A., Common functional principal components, Annals of Statistics, 37, 1-34 (2009) · Zbl 1169.62057 [4] Bosq, D., Linear Processes in Functional Spaces (2000), Springer: Springer New York [6] Dauxois, J.; Pousse, A.; Romain, Y., Asymptotic theory for the principal component analysis of a vector random functionsome applications to statistical inference, Journal of Multivariate Analysis, 12, 136-154 (1982) · Zbl 0539.62064 [7] Dehling, H.; Philipp, W., Almost sure invariance principles for weakly dependent vector-values random variables, Annals of Probability, 10, 689-701 (1982) · Zbl 0487.60006 [8] (Ferraty, F., Recent Advances in Functional Data Analysis and Related Topics (2011), Physica-Verlag: Physica-Verlag Berlin-Heidelberg) · Zbl 1220.62003 [9] Fremdt, S.; Steinebach, J.; Horváth, L.; Kokoszka, P., Testing the equality of covariance operators in functional samples, Scandinavian Journal of Statistics, 40, 138-152 (2013) · Zbl 1259.62031 [10] Galeano, P.; Peña, D., Covariance changes detection in multivariate time series, Journal of Statistical Planning and Inference, 137, 194-211 (2009) · Zbl 1098.62114 [11] Hall, P.; Hosseini-Nasab, M., On properties of functional principal components analysis, Journal of the Royal Statistical Society: Series B, 68, 109-126 (2006) · Zbl 1141.62048 [12] Hall, P.; Hosseini-Nasab, M., Theory for high-order bounds in functional principal components analysis, Mathematical Proceedings of the Cambridge Philosophical Society, 146, 225-256 (2009) · Zbl 1153.62050 [13] Horváth, L.; Kokoszka, P., Inference for Functional Data with Applications (2012), Springer: Springer Heidelberg · Zbl 1279.62017 [14] Horváth, L.; Kokoszka, P.; Steinebach, J., Testing for changes in multivariate dependent observations with an application to temperature changes, Journal of Multivariate Analysis, 68, 96-119 (1999) · Zbl 0962.62042 [15] Horváth, L.; Hušková, M.; Kokoszka, P., Testing the stability of the functional autoregressive process, Journal of Multivariate Analysis, 101, 352-367 (2010) · Zbl 1178.62099 [16] Panaretos, V. M.; Kraus, D.; Maddocks, J. H., Second-order comparison of Gaussian random functions and the geometry of DNA minicircles, Journal of the Acoustical Society of America, 105, 670-682 (2010) · Zbl 1392.62162 [18] Wied, D.; Krämer, W.; Dehling, H., Testing for a change in correlation at unknown point in time using an extended functional delta method, Econometric Theory, 28, 570-589 (2012) · Zbl 1239.91187 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.