Extremes of moving averages and moving maxima on a regular lattice

• Autorzy: Basrak B. , Tafro A.
• Języki publikacji: EN

Abstrakty

EN

We study the extremal behaviour of spatial moving averages and moving maxima on a regular discrete grid. Our main assumption is that these random fields are stationary and regularly varying with the tail index α > 0. Using the asymptotic theory for point processes we characterise the limiting behaviour of their extremes over an increasing grid. Our approach builds on the results of Davis and Resnick concerning linear processes. By analogy to the analysis of time series data, an appropriate Hill estimator of the tail index can be defined.We exhibit a sufficient condition for the consistency of this estimator in a certain class of spatial lattice models. Finally, we show that this condition holds for the models in our title.

Słowa kluczowe

EN

regular variation; point processes; stationary random fields; regular grid; extreme value theory

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 1
• Strony: 61--79
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Basrak B.

• University of Zagreb, Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia

autor

Tafro A.

• University of Zagreb, Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia

Bibliografia

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• [4] R. A. Davis , C. Klüppelberg, and C. Steinkohl, Max-stable processes for modeling extremes observed in space and time, preprint, arXiv: 1107.4464 (2011).
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• [12] S. I. Resnick, Extreme Values, Regular Variation, and Point Processes, Springer, New York 2008.
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• [15] K. F. Turkman, A note on the extremal index for space-time processes, J. Appl. Probab. 43 (2006), pp. 114-126.
• [16] K. F. Turkman, M. A. A. Turkman, and J. M. Pereira, Asymptotic models and inference for extremes of spatio-temporal data, Extremes 13 (2010), pp. 375-397.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).