Abstract
Let {X n , n≥1} be a sequence of independent Gaussian random vectors in Rd d≥2. In this paper an asymptotic evaluation of P{max1≤i≤n X i ≤a n Z+b n } with Z another Gaussian random vector is obtained for a n, b n ∈R d two vectors obeying certain conditions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bischoff, W., Hashorva, E., Hüsler, J., and Miller, F. The large deviation of the Kolmogorov test for a Brownian bridge with general trend with applications to change-point problems in regression models. Preprint Nr. 01115. Fakultät für Mathematik, Universität Karlsruhe.
de Haan, L., “Extremes in higher dimensions: the model and some statistics,” Proc. 45th Sess. Int. Statist. Inst. paper 26.3, (1985).
Gnedin, A.V., “On multivariate extremal processes,” J. Multivariate Anal. 46(2), 207–213, (1993).
Gnedin, A.V., “On the best choice problem with dependent criteria,” J. Appl. Probab. 31, 221–234, (1994).
Gnedin, A.V., “Records from a multivariate normal sample,” Statist. Probab. Lett. 39, 11–15, (1998).
Hashorva, E., “Remarks on the domination of maxima,” Statist. Probab. Lett. 60, 101–109, (2002).
Hashorva, E. and Hüsler, J., “On asymptotics of multivariate integrals with applications to records,” Stochastic Models 18(1), 41–69, (2002).
Hashorva, E. and Hüsler, J., Asymptotic Independence/Dependence of Triangular Arrays of Random Vectors, Preprint, (1999).
Hashorva, E. and Hüsler, J., “On multivariate Gaussian tails,” To appear in Ann. Inst. Statist. Math. (2003).
Kallenberg, O., Foundations of Modern Probability, Springer, New York, 1997.
Leadbetter, M.R., Lindgren, G., and Rootzén, H., Extremes and Related Properties of Random Sequences and Processes, Springer, Berlin, 1983.
Ledford, W.A. and Tawn, A.J., “On the tail concomitant behavior for extremes,” Adv. Appl. Prob. 30, 197–215, (1998).
Resnick, S.I., Extreme Values, Regular Variation and Point Processes, Springer, New York, 1987.
Stanislaw, J.S. and Werner, E., “A nonsymmetric correlation inequality for Gaussian measure,” J. Multivariate Anal. 68(2), 193–211, (1999).
Tong, Y.L., The Multivariate Normal Distribution, Springer, Berlin, 1990.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hashorva, E. Asymptotics of Dominated Gaussian Maxima. Extremes 5, 353–368 (2002). https://doi.org/10.1023/A:1025124225680
Issue Date:
DOI: https://doi.org/10.1023/A:1025124225680