ArticleOriginal scientific text
Title
Extremes in multivariate stationary normal sequences
Authors 1
Affiliations
- Technical University of Kielce, Al. 1000-Lecia Państwa Polskiego 7, 25-314 Kielce, Poland
Abstract
This paper deals with a weak convergence of maximum vectors built on the base of stationary and normal sequences of relatively strongly dependent random vectors. The discussion concentrates on the normality of limits and extends some results of McCormick and Mittal [4] to the multivariate case.
Keywords
stationary normal sequences, extreme order statistics
Bibliography
- S. M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist. 35 (1964), 502-516.
- J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York, 1978.
- M. R. Leadbetter, G. Lindgren and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
- W. P. McCormick and Y. Mittal, On weak convergence of the maximum, Techn. Report No 81, Dept. of Statist. Stanford Univ., 1976.
- Y. Mittal and D. Ylvisaker, Limit distributions for the maxima of stationary Gaussian processes, Stochastic Process. Appl. 3 (1975), 1-18.
- M. Wiśniewski, Extreme order statistics in an equally correlated Gaussian array, Appl. Math. (Warsaw) 22 (1994), 193-200.
Pages:
375-379
Main language of publication
English
Received
1997-10-05
Published
1998
Exact and natural sciences