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The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.

Approximations et majorations optimales des statistiques d'ordre d'un échantillon

G. Caraux, O. Gascuel (1991)

Revue de Statistique Appliquée

Asymptotic behaviour of the probability-weighted moments and penultimate approximation

Jean Diebolt, Armelle Guillou, Rym Worms (2003)

ESAIM: Probability and Statistics

The P.O.T. (Peaks-Over-Threshold) approach consists of using the Generalized Pareto Distribution (GPD) to approximate the distribution of excesses over a threshold. We use the probability-weighted moments to estimate the parameters of the approximating distribution. We study the asymptotic behaviour of these estimators (in particular their asymptotic bias) and also the functional bias of the GPD as an estimate of the distribution function of the excesses. We adapt penultimate approximation results...

Asymptotic behaviour of the probability-weighted moments and penultimate approximation

Jean Diebolt, Armelle Guillou, Rym Worms (2010)

ESAIM: Probability and Statistics

Bounds and asymptotic expansions for the distribution of the maximum of a smooth stationary gaussian process

Jean-Marc Azaïs, Christine Cierco-Ayrolles, Alain Croquette (1999)

ESAIM: Probability and Statistics

Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process

Jean-Marc Azaïs, Christine Cierco-Ayrolles, Alain Croquette (2010)

ESAIM: Probability and Statistics

This paper uses the Rice method [18] to give bounds to the distribution of the maximum of a smooth stationary Gaussian process. We give simpler expressions of the first two terms of the Rice series [3,13] for the distribution of the maximum. Our main contribution is a simpler form of the second factorial moment of the number of upcrossings which is in some sense a generalization of Steinberg et al.'s formula ([7] p. 212). Then, we present a numerical application and asymptotic expansions...

Competing particle systems evolving by I.I.D. Increments.

Shkolnikov, Mykhaylo (2009)

Electronic Journal of Probability [electronic only]

Compound Poisson approximation for extremes of moving minima in arrays of independent random variables

Jadwiga Dudkiewicz (1998)

Applicationes Mathematicae

We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.

Corners and records of the Poisson process in quadrant.

Gnedin, Alexander (2008)

Electronic Communications in Probability [electronic only]

Derrida's generalised random energy models 1 : models with finitely many hierarchies

Anton Bovier, Irina Kurkova (2004)

Annales de l'I.H.P. Probabilités et statistiques

Derrida's generalized random energy models 2 : models with continuous hierarchies

Anton Bovier, Irina Kurkova (2004)

Annales de l'I.H.P. Probabilités et statistiques

Detecting Changes in a Multivariate Renewal Process.

Josef Steinebach, Vera R. Eastwood (1997)

Metrika

Detection of transient change in mean – a linear behavior inside epidemic interval

Daniela Jarušková (2011)

Kybernetika

A procedure for testing occurrance of a transient change in mean of a sequence is suggested where inside an epidemic interval the mean is a linear function of time points. Asymptotic behavior of considered trimmed maximum-type test statistics is presented. Approximate critical values are obtained using an approximation of exceedance probabilities over a high level by Gaussian fields with a locally stationary structure.

Estimates of some probabilities in multidimensional convex records

Marek Kałuszka (1995)

Applicationes Mathematicae

Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability $p_{n} (k)$ that in a sequence of random vectors $X_{1}$ ,..., $X_{n}$ there are exactly k records.

Estimation for heavy tailed moving average process

Hakim Ouadjed, Tawfiq Fawzi Mami (2018)

Kybernetika

In this paper, we propose two estimators for a heavy tailed MA(1) process. The first is a semi parametric estimator designed for MA(1) driven by positive-value stable variables innovations. We study its asymptotic normality and finite sample performance. We compare the behavior of this estimator in which we use the Hill estimator for the extreme index and the estimator in which we use the t-Hill in order to examine its robustness. The second estimator is for MA(1) driven by stable variables innovations...

Estimation of second order parameters using probability weighted moments

Julien Worms, Rym Worms (2012)

ESAIM: Probability and Statistics

The P.O.T. method (Peaks Over Threshold) consists in using the generalized Pareto distribution (GPD) as an approximation for the distribution of excesses over a high threshold. In this work, we use a refinement of this approximation in order to estimate second order parameters of the model using the method of probability-weighted moments (PWM): in particular, this leads to the introduction of a new estimator for the second order parameter ρ, which will be compared to other recent estimators through...

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