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A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing

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Bücher, Axel [UCL]

This article investigates weak convergence of the sequential d-dimensional empirical process under strong mixing.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2015
Language Anglais
Journal information "Journal of Theoretical Probability" - Vol. 28, no. 3, p. 1028-1037 (2015)
Peer reviewed yes
Publisher Springer New York LLC (New York)
issn 0894-9840
e-issn 1572-9230
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords Multivariate sequential empirical processes ; Weak convergence ; Strong alpha mixing ; Ottaviani’s inequality
Links
  1. Arcones M. A., Yu B., Central limit theorems for empirical andU-processes of stationary mixing sequences, 10.1007/bf02213360
  2. Bradley, R.C.: Introduction to Strong Mixing Conditions, vol. 1. Kendrick Press, Heber City, UT (2007)
  3. Dedecker, J., Merlevède, F., Rio, E.: Strong Approximation of the Empirical Distribution Function for Absolutely Regular Sequences in $${\bf R}^d$$ R d . Working paper (2013). http://hal.archives-ouvertes.fr/hal-00798305
  4. Dehling, H., Durieu, O., Tusche, M.: A Sequential Empirical CLT for Multiple Mixing Processes with Application to $${\cal B}$$ B -Geometrically Ergodic Markov Chains. arXiv:1303.4537 (2013)
  5. Dhompongsa, S.: A note of the almost sure approximation of the empirical process of weakly dependent random vectors. Yokohama Math. J. 32, 113–121 (1984)
  6. Doukhan Paul, Mixing, ISBN:9780387942148, 10.1007/978-1-4612-2642-0
  7. Doukhan Paul, Fermanian Jean-David, Lang Gabriel, An empirical central limit theorem with applications to copulas under weak dependence, 10.1007/s11203-008-9026-3
  8. Doukhan, P., Massart, P., Rio, E.: The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincaré Probab. Stat. 30(1), 63–82 (1994)
  9. Doukhan, P., Massart, P., Rio, E.: Invariance principles for absolutely regular empirical processes. Ann. Inst. H. Poincaré Probab. Stat. 31(2), 393–427 (1995)
  10. Durieu Olivier, Tusche Marco, An Empirical Process Central Limit Theorem for Multidimensional Dependent Data, 10.1007/s10959-012-0450-3
  11. Inoue Atsushi, TESTING FOR DISTRIBUTIONAL CHANGE IN TIME SERIES, 10.1017/s0266466601171057
  12. Rio, E.: Théorie Asymptotique des Processus aléatoires Faiblement Dépendants. Springer, Berlin (2000)
  13. Rosenblatt M., A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION, 10.1073/pnas.42.1.43
  14. Shao Qi-Man, Yu Hao, Weak convergence for weighted empirical processes of dependent sequences, 10.1214/aop/1041903220
  15. Shao Xiaofeng, A self-normalized approach to confidence interval construction in time series : Confidence Interval Construction in Time Series, 10.1111/j.1467-9868.2009.00737.x
  16. van der Vaart Aad W., Wellner Jon A., Weak Convergence and Empirical Processes, ISBN:9781475725476, 10.1007/978-1-4757-2545-2
  17. Yoshihara Ken-ichi, Weak convergence of multidimensional empirical processes for strong mixing sequences of stochastic vectors, 10.1007/bf00538353
Bibliographic reference Bücher, Axel. A Note on Weak Convergence of the Sequential Multivariate Empirical Process Under Strong Mixing. In: Journal of Theoretical Probability, Vol. 28, no. 3, p. 1028-1037 (2015)
Permanent URL http://hdl.handle.net/2078.1/151303