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Asymptotic Extremal Distribution for Non-Stationary, strongly-dependent data

Advances in Pure Mathematics 2022年第8期12卷 479-489页

作者： Carolina Crisci Gonzalo Perera Departamento Modelización Estadística de Datos e Inteligencia Artificial (MEDIA) CURE Rocha Universidad de la República Montevideo Uruguay

Fisher-Tippet-Gnedenko classical theory shows that the normalized maximum of n iid random variables with distribution F belonging to a very wide class of functions, converges in law to an extremal distribution H, that is determined by the tail of F. Extensions of this theory from the iid case to stationary and weak dependent sequences are well known from the work of Leadbetter, Lindgreen and Rootzén. In this paper, we present a very simple class of random processes that runs from iid sequences to non-stationary and strongly dependent processes, and we study the asymptotic behavior of its normalized maximum. More interesting, we show that when the process is strongly dependent, the asymptotic distribution is no longer an extremal one, but a mixture of extremal distributions. We present very simple theoretical and simulated examples of this result. This provides a simple framework to asymptotic approximations of extremes values not covered by classical extremal theory and its well-known extensions.

关键词： Extreme Events strongly dependent data Fisher-Tippet-Gnedenko Theory

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Goodness-of-Fit Test for Non-Stationary and strongly dependent Samples

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Advances in Pure Mathematics 2023年第5期13卷 226-236页

作者： Carolina Crisci Gonzalo Perera Lia Sampognaro Departamento Modelización Estadística de Datos e Inteligenica Artificial (MEDIA) CURE Rocha Universidad de la República Montevideo Uruguay

In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical process, which is much more complex than in the classical case. Applications to simulated data and discussion of the obtained results are provided. This is, to the best of our knowledge, the first result providing a general goodness of fit test for non-weakly dependent data.

关键词： Kolmogorov-Smirnov Test strongly dependent data Asymptotic Behavior of Empirical Processes

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Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

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Advances in Pure Mathematics 2023年第7期13卷 425-441页

作者： Carolina Crisci Gonzalo Perera Lia Sampognaro Departamento Modelización Estadística de Datos e Inteligenica Artificial (MEDIA) CURE Rocha Universidad de la República Rocha Uruguay

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

关键词： Mixture of Extremal Distributions strongly dependent data

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