EXTREMES OF ORDER STATISTICS OF STATIONARY GAUSSIAN PROCESSES

被引:3
作者
Zhao, Chunming [1 ]
机构
[1] Southwest Jiaotong Univ, Sch Math, Dept Stat, Xian Rd 999, Chengdu 611756, Sichuan, Peoples R China
来源
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND | 2018年 / 38卷 / 01期
关键词
Asymptotic; Gaussian processes; order statistic; stationarity; supremum; EXACT ASYMPTOTICS; CONJUNCTION; PROBABILITY;
D O I
10.19195/0208-4147.38.1.4
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Let {X-i(t); t >= 0}, 1 <= i <= n, be mutually independent and identically distributed centered stationary Gaussian processes. Under some mild assumptions on the covariance function, we derive an asymptotic expansion of P (sup(t subset of[0,xmr(u)]) X-(r)(t) <= u) as u -> infinity, where m(r)(u) = (P(sup(t is an element of[0,1]) X-(r)(t) > u))(-1) (1 + o(1)), and {X-(r)(t); t >= 0} is the rth order statistic process of {X-i(t); t >= 0}, 1 <= i; r <= n. As an application of the derived result, we analyze the asymptotics of supremum of the order statistic process of stationary Gaussian processes over random intervals.
引用
收藏
页码:61 / 75
页数:15
相关论文
共 14 条
  • [1] A NEW PROOF OF AN OLD RESULT BY PICKANDS
    Albin, J. M. P.
    Choi, H.
    [J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2010, 15 : 339 - 345
  • [2] An approximation to cluster size distribution of two Gaussian random fields conjunction with application to FMRI data
    Alodat, M. T.
    [J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (07) : 2331 - 2347
  • [3] Alodat MT, 2010, J APPL PROBAB, V47, P179
  • [4] Exact asymptotics of supremum of a stationary Gaussian process over a random interval
    Arendarczyk, Marek
    Debicki, Krzysztof
    [J]. STATISTICS & PROBABILITY LETTERS, 2012, 82 (03) : 645 - 652
  • [5] Bingham NH., 1989, REGULAR VARIATION
  • [6] Excursion probability of Gaussian random fields on sphere
    Cheng, Dan
    Xiao, Yimin
    [J]. BERNOULLI, 2016, 22 (02) : 1113 - 1130
  • [7] Debicki K., BERMANS INEQUALITY O
  • [8] Extremes of vector-valued Gaussian processes: Exact asymptotics
    Debicki, Krzysztof
    Hashorva, Enkelejd
    Ji, Lanpeng
    Tabis, Kamil
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2015, 125 (11) : 4039 - 4065
  • [9] On the probability of conjunctions of stationary Gaussian processes
    Debicki, Krzysztof
    Hashorva, Enkelejd
    Ji, Lanpeng
    Tabis, Kamil
    [J]. STATISTICS & PROBABILITY LETTERS, 2014, 88 : 141 - 148
  • [10] BONFERRONI INEQUALITIES
    GALAMBOS, J
    [J]. ANNALS OF PROBABILITY, 1977, 5 (04) : 577 - 581