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Title: Random fields and random sampling (English)
Author: Dias, Sandra
Author: Temido, Maria da Graça
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 55
Issue: 6
Year: 2019
Pages: 897-914
Summary lang: English
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Category: math
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Summary: We study the limiting distribution of the maximum value of a stationary bivariate real random field satisfying suitable weak mixing conditions. In the first part, when the double dimensions of the random samples have a geometric growing pattern, a max-semistable distribution is obtained. In the second part, considering the random field sampled at double random times, a mixture distribution is established for the limiting distribution of the maximum. (English)
Keyword: stationary random fields
Keyword: max-semistable laws
Keyword: random double sample size
MSC: 60G60
MSC: 60G70
idZBL: Zbl 07217218
idMR: MR4077136
DOI: 10.14736/kyb-2019-6-0897
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Date available: 2020-05-20T15:07:27Z
Last updated: 2020-08-26
Stable URL: http://hdl.handle.net/10338.dmlcz/148082
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Reference: [1] e, Castro, L. Canto, S., Dias,: Generalized Pickands' estimators for the tail index parameter and max-semistability..Extremes 14 (2011), 429-449. MR 2853110, 10.1007/s10687-010-0123-5
Reference: [2] e, Castro, L. Canto, S., Dias,, G., Temido, M.: Looking for max-semistability: A new test for the extreme value condition..J. Statist. Plann. Inference 141 (2011), 3005-3020. MR 2796007, 10.1016/j.jspi.2011.03.020
Reference: [3] e, Castro, L. Canto, S., Dias,, G., Temido, M.: Tail inference for a law in a max-semistable domain of attraction..Pliska Stud. Math. Bulgar. 19 (2009), 83-96. MR 2547733
Reference: [4] H., Choi,: Central Limit Theory and Extremes of Random Fields..PhD Thesis, Univ. of North Carolina at Chapel Hill 2002. MR 2702684
Reference: [5] H., Ferreira,: Extremes of a random number of variables from periodic sequences..J. Statist. Plann. Inference 4 (1995), 133-141. MR 1342090, 10.1016/0378-3758(94)00082-4
Reference: [6] H., Ferreira,, L., Pereira,: How to compute the extremal index of stationary random fields..Statist. Probab. Lett. 78 (2008), 1301-1304. MR 2444320, 10.1016/j.spl.2007.11.025
Reference: [7] H., Ferreira,, L., Pereira,: Point processes of exceedances by random fields..J. Statist. Plann. Inference 142 (2012), 773-779. MR 2853583, 10.1016/j.jspi.2011.09.012
Reference: [8] A., Freitas,, J., Hüsler,, G., Temido, M.: Limit laws for maxima of a stationary random sequence with random sample size..Test 21 (2012), 116-131. MR 2912974, 10.1007/s11749-011-0238-2
Reference: [9] J., Galambos,: The Asymptotic Theory of Extreme Order Statistics..John Wiley, New York 1978. MR 0489334
Reference: [10] V., Grinevich, I.: Max-semistable limit laws under linear and power normalizations..Theory Probab. Appl., 38 (1992), 640-650. MR 1317998, 10.1137/1138064
Reference: [11] E., Hashorva,, O., Seleznjev,, Z., Tan,: Approximation of maximum of Gaussian random fields..J. Math. Anal. Appl. 457 (2018), 841-867. MR 3702733, 10.1016/j.jmaa.2017.08.040
Reference: [12] R., Leadbetter, M., G., Lindgren,, H., Rootzén,: Extremes and Related Properties of Random Sequences and Processes..Springer-Verlag, Berlin 1983. Zbl 0518.60021, MR 0691492, 10.1007/978-1-4612-5449-2
Reference: [13] R., Leadbetter, M., H., Rootzén,: On extreme values in stationary random fields..In: Stochastic Processes and Related Topics (I. Karatzas, B. S. Rajput, and M. S. Taqqu, eds.), Birkhäuser, Boston 1998, pp. 275-285. MR 1652377, 10.1007/978-1-4612-2030-5\_15
Reference: [14] E., Pancheva,: Multivariate max-semistable distributions..Theory Probab. Appl. 18 (1992), 679-705.
Reference: [15] L., Pereira,: On the extremal behavior of a nonstationary normal random field..J. Statist. Plann. Inference 140 (2010), 3567-3576. MR 2659878, 10.1016/j.jspi.2010.04.049
Reference: [16] L., Pereira,, H., Ferreira,: Extremes of quasi-independent random fields and clustering of high values..In: Proc. 8th WSEAS International Conference on Applied Mathematics, WSEAS, Tenerife 2005, pp. 104-109. MR 2194385
Reference: [17] L., Pereira,, H., Ferreira,: Limiting crossing probabilities of random fields..J. Appl. Probab. 43 (2006), 884-891. MR 2274809, 10.1017/s0021900200002199
Reference: [18] L., Pereira,, Z., Tan,: Almost sure convergence for the maximum of nonstationary random fields..J. Theoret. Probab. 30 (2017), 996-1013. MR 3687247, 10.1007/s10959-015-0663-3
Reference: [19] A., Rényi,: On mixing sequences of sets..Acta Math. Acad. Sci. Hungar. 9 (1958), 215-228. MR 0098161, 10.1007/bf02023873
Reference: [20] Z., Tan,: An almost sure limit theorem for the maxima of smooth stationary Gaussian processes..Statist. Probab. Lett. 83 (2013), 2135-2141. MR 3079057, 10.1016/j.spl.2013.05.034
Reference: [21] Z., Tan,: Asymptotics of maxima and sums for a type of strongly dependent isotropic Gaussian random fields..Comm. Statist. Theory Methods 47 (2018), 5013-5028. MR 3833878, 10.1080/03610926.2017.1383430
Reference: [22] Z., Tan,, Y., Wang,: Almost sure asymptotics for extremes of non-stationary Gaussian random fields..Chinese Ann. Math. Ser. B 35 (2014), 125-138. MR 3160785, 10.1007/s11401-013-0810-z
Reference: [23] G., Temido, M., e, Castro, L. Canto: Max-semistable laws in extremes of stationary random sequences..Theory Probab. Appl. 47 (2003), 365-374. MR 2003209, 10.1137/tprbau000047000002000365000001
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