On the Maximum and Minimum of a Stationary Random Field

Conference paper

DOI: 10.1007/978-3-642-34904-1_35

Part of the Studies in Theoretical and Applied Statistics book series (STAS)
Cite this paper as:
Pereira L. (2013) On the Maximum and Minimum of a Stationary Random Field. In: Lita da Silva J., Caeiro F., Natário I., Braumann C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics. Springer, Berlin, Heidelberg

Abstract

We determine the class of nondegenerate joint-limiting distributions for the maximum and minimum of stationary random fields \(\mathbf{X} = \left \{X_{\mathbf{n}}\right \}_{\mathbf{n\in {\mathbb{N}}^{2}}}\) satisfying a long-range dependence restriction for each coordinate direction at a time. Unlike the classical result for i.i.d. random fields the maximum and minimum of X may be asymptotically dependent. We also give a sufficient condition for the asymptotic independence of the maximum and minimum. Additional conditions are given in order to obtain the asymptotic independence of the locations of maximum and minimum.

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of Beira InteriorCovilhãPortugal

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