Czasopismo
2024
|
Vol. 44, Fasc. 1
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29-- 50
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, we derive the asymptotic distributions for the maxima of two types of Gaussian functions, including a χ-random sequence and a Gaussian order statistics sequence subject to missing observations, where the Gaussian functions are generated by stationary Gaussian sequences with covariance functions rn satisfying rn log n → γ ∈[0,∞) as n →∞.
Czasopismo
Rocznik
Tom
Strony
29-- 50
Opis fizyczny
Bibliogr. 39 poz.
Twórcy
autor
- College of Data Science Jiaxing University Jiaxing 314001, PR China, zsc209@163.com
autor
- College of Data Science Jiaxing University Jiaxing 314001, PR China, tzq728@163.com
Bibliografia
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- [6] K. D˛ebicki, E. Hashorva, K. Ji, and L. Tabi´s, On the probability of conjunctions of stationary Gaussian processes, Statist. Probab. Lett. 88 (2014), 141-148.
- [7] K. D˛ebicki, E. Hashorva, L. Ji, and C. Ling, Extremes of order statistics of stationary processes, Test 24 (2015), 229-248.
- [8] K. D˛ebicki, E. Hashorva, L. Ji, and C. Ling, Comparison inequality for order statistics of Gaussian arrays, Latin Amer. J. Probab. Math. Statist. 14 (2017), 93-116.
- [9] L. Glavaš and P. Mladenovi´c, Extreme values of linear processes with heavy-tailed innovations and missing observations, Extremes 23 (2020), 547-567.
- [10] L. Glavaš, P. Mladenovi´c, and G. Samorodnitsky, Extreme values of the uniform order 1 autoregressive processes and missing observations, Extremes 20 (2017), 671-690.
- [11] E. Hashorva, Z. Peng, and Z. Weng, On Piterbarg theorem for maxima of stationary Gaussian sequences, Lithuanian Math. J. 53 (2013), 280-292.
- [12] E. Hashorva and Z. Weng, Maxima and minima of complete and incomplete stationary sequences, Stochastics 86 (2014), 707-720.
- [13] D. Jarušková and V. Piterbarg, Log-likelihood ratio test for detecting transient change, Statist. Probab. Lett. 81 (2011), 552-559.
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- [15] T. Krajka and Z. Rychlik, The limiting behaviour of sums and maximums of iid random variables from the viewpoint of different observers, Probab. Math. Statist. 34 (2014), 237-252.
- [16] M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.
- [17] Y. Li and Z. Tan, The limit properties of maxima of stationary Gaussian sequences subject to random replacing, Mathematics 11 (2023), art. 3155.
- [18] C. Ling and Z. Tan. On maxima of chi-processes over threshold dependent grids, Statistics 50 (2016), 579-595.
- [19] C. Ling, Z. Peng, and Z. Tan, Extremes on different grids and continuous time of stationary processes, J. Math. Anal. Appl. 461 (2018), 150-168.
- [20] Y. Lu and Z. Peng, Maxima and minima of homogeneous Gaussian random fields over continuous time and uniform grids, Stochastics 92 (2020), 165-192.
- [21] P. Mladenovi´c and V. I. Piterbarg, On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences, Stochastic Process. Appl. 116 (2006), 1977-1991.
- [22] Z. Panga and L. Pereira, On the maxima and minima of complete and incomplete samples from nonstationary random fields, Statis. Probab. Lett. 137 (2018), 124-134.
- [23] Z. Peng, L. Cao, and S. Nadarajah, Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences, J. Multivariate Anal. 101 (2010), 2641-2647.
- [24] Z. Peng, J. Tong, and Z. Weng, Exceedances point processes in the plane of stationary Gaussian sequences with data missing, Statist. Probab. Lett. 149 (2019), 73-79.
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- [29] J. Sun and Z. Tan, Extremes of dependent chi-processes attracted by the Brown-Resnick process, Acta Math. Sci. 44 (2024), 686-701.
- [30] Z. Tan, On the maxima of continuous and discrete time Gaussian order statistics processes, Sci. Sinica Math. 48 (2018), 623-642.
- [31] Z. Tan and E. Hashorva, Exact asymptotics and limit theorems for supremum of stationary χ-processes over a random interval, Stochastic Process. Appl. 123 (2013), 2983-2998.
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- [33] Z. Tan and L. Tang, The dependence of extreme values of discrete and continuous time strongly dependent Gaussian processes, Stochastics 86 (2014), 60-69.
- [34] Z. Tan and Y. Wang, Some asymptotic results on extremes of incomplete samples, Extremes 15 (2012), 319-332.
- [35] B. Tong and Z. Peng, On almost sure max-limit theorems of complete and incomplete samples from stationary sequences, Acta Math. Sinica (English Ser.) 27 (2011), 1323-1332.
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- [37] Z. Xu, Z. Tan, and L. Tang, Approximation of the maximum of storage process with fractional Brownian motion as input, Statist. Probab. Lett. 140 (2018), 147-159.
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- [39] S. Zheng and Z. Tan, On the maxima of nonstationary random fields subject to missing observations, Comm. Statist. Theory Methods (online, 2023).
Typ dokumentu
Bibliografia
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