Buriticá, Gloria Naveau, Philippe

Heavy rainfall distributional modeling is essential in any impact studies linked to the water cycle, e.g.\ flood risks. Still, statistical analyses that both take into account the temporal and multivariate nature of extreme rainfall are rare, and often, a complex de-clustering step is needed to make extreme rainfall temporally independent. A natura...

Buriticá, Gloria Naveau, Philippe

First, we complement the case study of heavy rainfall in France by implementing Pareto-based methods using declustering techniques. Second, we develop on the asymptotic theory of the stable sums method. To prove Theorem 6.1, we give a more general statement and prove the multivariate central limit theory of regularly varying time series with unit (...

Zhang, Xiuzhen Zhang, Riquan Lu, Zhiping
Published in
Frontiers in Physics

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical like...

Sadefo Kamdem, Jules GUEMDJO KAMDEM, Babel Raïssa OUGOUYANDJOU, Carlos

The main purpose of this work is to contribute to the study of set-valued random variablesby providing a kind of Wold decomposition theorem for interval-valued processes. As theset of set-valued random variables is not a vector space, the Wold decomposition theorem asestablished in 1938 by Herman Wold is not applicable for them. So, a notion of pse...

Duthinh, Dat Pintar, Adam L. Simiu, Emil
Published in
Engineering structures

Estimating properties of the distribution of the peak of a stationary process from a single finite realization is a problem that arises in a variety of science and engineering applications. Further, it is often the case that the realization is of length T while the distribution of the peak is sought for a different length of time, T 1 > T . Current...

Berghaus, Betina Bücher, Axel

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the ...

Bücher, Axel Segers, Johan

The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying assumptions: the block maxima should be distributed according to an extreme-value distribution and the sample of bl...

Bücher, Axel Segers, Johan

The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are an independent random sample of an extreme value distribution. In practice however, block sizes are finite, so...

Ombao, Hernando Raz, Jonathan von Sachs, Rainer Guo, Wensheng
Published in
Annals of the Institute of Statistical Mathematics

We propose a new model for non-stationary random processes to represent time series with a time-varying spectral structure. Our SLEX model can be considered as a discrete time-dependent Cramér spectral representation. It is based on the so-called Smooth Localized complex EXponential basis functions which are orthogonal and localized in both time an...

Chakrabarty, S. Chopin, M. Darrat, A.
Published in
Marketing Letters

Knowledge of consumer attitudes and expectations is an indispensable marketing tool and may be useful for predicting changes in consumer spending and saving patterns. However, most empirical research on the value of consumer confidence (sentiment) indexes for forecasting future buyer behavior has focused on the statistical correlation between these...