Extremes in multivariate stationary normal sequences

Wiśniewski, Mateusz

doi:10.4064/am-25-3-375-379

Cited by 4 publications

(4 citation statements)

References 4 publications

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“…For more details, see Leadbetter et al (1983). For the limiting distribution of the extremes of vector Gaussian sequences, see James, James, and Qi (2007) and Wiśniewski (1994Wiśniewski ( , 1996Wiśniewski ( , 1998.…”

Section: Introductionmentioning

confidence: 99%

Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples

Zhong

Chen

2012

Journal of the Korean Statistical Society

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a b s t r a c tLet {X n , n ≥ 1} be a sequence of d-dimensional stationary Gaussian vectors, and let M n denote the maxima of {X k , 1 ≤ k ≤ n}. Suppose that there are missing data in each component of X k and let  M n denote the maxima of the observed variables. In this paper, we study the asymptotic distribution of the random vector (  M n , M n ) as the correlation and cross-correlation satisfy strongly dependent conditions.

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Section: Introductionmentioning

confidence: 99%

Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples

Zhong

Chen

2012

Journal of the Korean Statistical Society

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“…For the limiting distribution of the extremes of vector Gaussian sequences, see [3,[12][13][14]. The aim of this note is to establish the joint limiting distribution of the maxima of complete and incomplete samples of stationary Gaussian vector sequences under some weakly and strongly dependent conditions similar to those of [9,8], where the univariate case is considered.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences

Peng

Cao

Nadarajah

2010

Journal of Multivariate Analysis

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a b s t r a c tLet (X n ) be a sequence of d-dimensional stationary Gaussian vectors, and let M n denote the partial maxima of {X k , 1 ≤ k ≤ n}. Suppose that there are missing data in each component of X k and let M n denote the partial maxima of the observed variables. In this note, we study two kinds of asymptotic distributions of the random vector ( M n , M n ) where the correlation and cross-correlation satisfy some dependence conditions.

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“…To our knowledge, this is the first paper to discuss the topic in the multivariate setting. Our multivariate maximum is defined as the vector of coordinatewise maxima, which was used in earlier work on the limit distribution of extremes for a multivariate Gaussian sequence; e.g., Amram [1], Husler [10], Husler and Schupbach [11], Wisniewski [18,19], to mention a few. The existence of limit distributions of the maximum is shown in these references under the multivariate analogues of conditions…”

Section: Introductionmentioning

confidence: 99%

Limit distribution of the sum and maximum from multivariate Gaussian sequences

James

2007

Journal of Multivariate Analysis

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In this paper we study the asymptotic joint behavior of the maximum and the partial sum of a multivariate Gaussian sequence. The multivariate maximum is defined to be the coordinatewise maximum. Results extend univariate results of McCormick and Qi. We show that, under regularity conditions, if the maximum has a limiting distribution it is asymptotically independent of the partial sum. We also prove that the maximum of a stationary sequence, when normalized in a special sense which includes subtracting the sample mean, is asymptotically independent of the partial sum (again, under regularity conditions). The limiting distributions are also obtained.

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Extremes in multivariate stationary normal sequences

Cited by 4 publications

References 4 publications

Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples

Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples

Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences

Limit distribution of the sum and maximum from multivariate Gaussian sequences

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