On asymptotics of multivariate integrals with applications to records

Details

Serval ID
serval:BIB_0696E30FDCCA
Type
Article: article from journal or magazin.
Collection
Publications
Title
On asymptotics of multivariate integrals with applications to records
Journal
Stochastic Models
Author(s)
Hashorva E., Hüsler J.
ISSN
1532-6349
1532-4214 ([electronic])
Publication state
Published
Issued date
2002
Peer-reviewed
Oui
Volume
18
Number
1
Pages
41-69
Language
english
Abstract
Let {X-n,n greater than or equal to 1} be a sequence of iid. Gaussian random vectors in R-d, d greater than or equal to 2, with nonsingular distribution function F. In this paper the asymptotics for the sequence of integrals I-F,I-n(G(n)) := n integral(Rd)G(n)(n-1)(X) dF(X) is considered with G(n) some distribution function on R-d. In the case G(n) = F the integral I-F,I-n(F)/n is the probability that a record occurs in X-1,..., X-n at index n. (1) obtained lower and upper asymptotic bounds for this case, whereas (2) showed the rate of convergence if d = 2. In this paper we derive the exact rate of convergence of I-F,I-n(G(n)) for d greater than or equal to 2 under some restrictions on the distribution function Gn. Some related results for multivariate Gaussian tails are discussed also.
Keywords
Exact asymptotics, Records, Extreme value distribution, Gaussian sequences, Quadratic programming
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Create date
03/09/2010 13:06
Last modification date
20/08/2019 12:28
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