Distance Covariance for Stochastic Processes

• Autorzy: Matsui M. , Mikosch T. , Samorodnitsky G.

Identyfikatory

DOI

10.19195/0208-4147.37.2.9

• Języki publikacji: EN

Abstrakty

EN

The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analog of the distance covariance for two stochastic processes defined on some interval. Their empirical analogs can be used to test the independence of two processes.

Słowa kluczowe

EN

empirical characteristic function; distance covariance; stochastic process; test of independence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 355--372
• Opis fizyczny: Bibliogr. 9 poz., wykr.

Twórcy

autor

Matsui M.

• Department of Business Administration, Nanzan University, 18 Yamazato-cho, Showa-ku, Nagoya 466-8673, Japan

autor

Mikosch T.

• Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

autor

Samorodnitsky G.

• School of Operations Research and Information Engineering, Cornell University, 220 Rhodes Hall, Ithaca, NY 14853, U.S.A.

Bibliografia

• [1] R. A. Davis, M. Matsui, T. Mikosch, and P. Wan, Applications of distance correlation to time series, Bernoulli (to appear).
• [2] A. Feuerverger, A consistent test for bivariate dependence, Internat. Statist. Rev. 61 (1993), pp. 419-433.
• [3] J. Hoffmann-Jørgensen, Probability with a View Towards Statistics, Chapman & Hall, New York 1994.
• [4] F. Lavancier, A. Philippe, and D. Surgailis, Covariance function of vector self-similar processes, Statist. Probab. Lett. 79 (2009), pp. 2415-2421.
• [5] R. Lyons, Distance covariance in metric spaces, Ann. Probab. 41 (2013), pp. 3284-3305.
• [6] G. J. Székely and M. L. Rizzo, Brownian distance covariance, Ann. Appl. Stat. 3 (2009), pp. 1236-1265.
• [7] G. J. Székely and M. L. Rizzo, The distance correlation t-test of independence in high dimension, J. Multivariate Anal. 117 (2013), pp. 193-213.
• [8] G. J. Székely and M. L. Rizzo, Partial distance correlation with methods for dissimilarities, Ann. Statist. 42 (2014), pp. 2382-2412.
• [9] G. J. Székely, M. L. Rizzo, and N. K. Bakirov, Measuring and testing dependence by correlation of distances, Ann. Statist. 35 (2007), pp. 2769-2794.

Uwagi

The authors of this paper would like to congratulate Tomasz Rolski on his 70th birthday.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).