Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2023 | Vol. 43, Fasc. 2 | 247--262
Tytuł artykułu

Point process of clusters for a stationary Gaussian random field on a lattice

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is well established that the normalized exceedances resulting from a standard stationary Gaussian triangular array at high levels follow a Poisson process under the Berman condition. To model frequent cluster phenomena, we consider the asymptotic distribution of the point process of clusters for a Gaussian random field on a lattice. Our analysis demonstrates that the point process of clusters also converges to a Poisson process in distribution, provided that the correlations of the Gaussian random field meet certain conditions. Additionally, we provide a numerical example to illustrate our theoretical results.
Wydawca

Rocznik
Strony
247--262
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • School of Science, Southwest Petroleum University, Chengdu, 610500, P.R. China, uyingyin93@163.com
autor
  • School of Statistics, Southwestern University of Finance and Economics, Chengdu, 611130, P.R. China, guojinhui94@163.com
Bibliografia
  • [1] P. Abbrahamsen, A review of Gaussian random fields and correlation functionals, Norwegian Computing Center, Oslo, 1997.
  • [2] P. Albin, E. Hashorva, L. Ji and C. Ling, Extremes and limit theorems for difference of chi-type processes, ESAIM Probab. Statist. 20 (2016), 349-366.
  • [3] M. Alodat, An approximation to cluster size distribution of two Gaussian random fields conjunction with application to FMRI data, J. Statist. Planning Inference 141 (2011), 2331-2347.
  • [4] J. Azaïs, S. Bercum, J. Fort, A. Lagnoux and P. Lé, Simultaneous confidence bands in curve prediction applied to load curves, J. Roy. Statist. Soc. Ser. C 59 (2010), 889-904.
  • [5] S. M. Berman, Asymptotic independence of the numbers of high and low level crossings of stationary Gaussian processes, Ann. Math. Statist. 42 (1971), 927-945.
  • [6] B. Brown and S. Resnick, Extreme values of independent stochastic processes, J. Appl. Probab. 14 (1997), 732-739.
  • [7] J. Cao and K. Worsley, Applications of random fields in human brain mapping, in: M. Moore (ed.), Spatial Statistics: Methodological Aspects and Applications, Springer, New York, 2001, 169-182.
  • [8] B. Das, S. Engelke and E. Hashorva, Extremal behavior of squared Bessel processes attracted by the Brown-Resnick process, Stochastic Process. Appl. 125 (2015), 780-796.
  • [9] K. Dębicki, E. Hashorva, L. Ji and C. Ling, Extremes of order statistics of stationary processes, TEST 24 (2015), 229-248.
  • [10] J. French, Confidence regions for level curves and a limit theorem for the maxima of Gaussian random fields, Ph.D. thesis, Colorado State Univ., Fort Collins, CO, 2009.
  • [11] J. P. French and R. A. Davis, The asymptotic distribution of the maxima of a Gaussian random field on a lattice, Extremes 16 (2013), 1-26.
  • [12] J. Guo and Y. Lu, Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays, Ann. Inst. Statist. Math. 75 (2023), 17-37.
  • [13] E. Hashorva, L. Peng and Z. Weng, Maxima of a triangular array of multivariate Gaussian sequence, Statist. Probab. Lett. 103 (2015), 62-72.
  • [14] E. Hashorva and Z. Weng, Limit laws for extremes of dependent stationary Gaussian arrays, Statist. Probab. Lett. 83 (2013), 320-330.
  • [15] T. Hsing, J. Hüsler and R.-D. Reiss, The extremes of a triangular array of normal random variables, Ann. Appl. Probab. 6 (1996), 671-686.
  • [16] Z. Kabluchko, M. Schlather and L. De Haan, Stationary max-stable fields associated to negative definite functions, Ann. Probab. 37 (2009), 2042-2065.
  • [17] M. R. Leadbetter, Extremes and local dependence in stationary sequences, Z. Wahrsch. Verw. Gebiete 65 (1983), 291-306.
  • [18] M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and Related Properties of Stationary Sequences and Processes, Springer, New York, 1983.
  • [19] C. Ling, Extremes of stationary random fields on a lattice, Extremes 22 (2019), 391-411.
  • [20] M. Oesting, Z. Kabluchko and M. Schlather, Simulation of Brown-Resnick processes, Extremes 15 (2012), 89-107.
  • [21] M. Pacifico, C. Genovese, I. Verdinelli and L. Wasserman, False discovery control for random fields, Journal of the American Statistical Association, 99 (2004), 1002-1014.
  • [22] L. Pereira, A. Martins and H. Ferreira, Clustering of high values in random fields, Extremes 20 (2017), 807-836.
  • [23] J. Taylor, K. Worsley and F. Gosselin, Maxima of discretely sampled random fields, with an application to ‘bubbles’, Biometrika 94 (2007), 1-18.
  • [24] L. Wasserman, All of Statistics: A Concise Course in Statistical Inference, Springer, 2004.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-51ab30f7-1f06-48d6-8583-0fff49082457
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.