Naslov
Extremes of moving averages and moving maxima on a regular lattice

Autori
Basrak, Bojan ; Tafro, Azra

Izvornik
Probability and Mathematical Statistics-Poland (0208-4147) 34 (2014), 1; 61-79

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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. Using the asymptotic theory for point processes we characterize the limiting behavior of their extremes over an increasing grid. Our approach builds on the results of Davis and Resnick concerning linear processes. In 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA