Displaying similar documents to “On the tail index estimation of an autoregressive Pareto process”

SURE shrinkage of gaussian paths and signal identification

Nicolas Privault, Anthony Réveillac (2011)

ESAIM: Probability and Statistics

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Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák, Michaela Prokešová (2016)

Applications of Mathematics

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We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate...

SURE shrinkage of Gaussian paths and signal identification

Nicolas Privault, Anthony Réveillac (2012)

ESAIM: Probability and Statistics

Similarity:

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.

Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes

Romain Azaïs, François Dufour, Anne Gégout-Petit (2013)

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

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This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions...

Moderate deviations for the Durbin–Watson statistic related to the first-order autoregressive process

S. Valère Bitseki Penda, Hacène Djellout, Frédéric Proïa (2014)

ESAIM: Probability and Statistics

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The purpose of this paper is to investigate moderate deviations for the Durbin–Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate...

Trend estimation problems in time-series analysis

E. Pleszczyńska

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CONTENTS1. Introduction............................................................................................................................................. 52. F-estimators........................................................................................................................................... 63. The role of the tests J* and T* in polynomial trend estimation problems.................................. 124. Testing the equivalence of two linear processes..............................................................................

Sequential estimation in processes with independent increments

S. Trybuła

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CONTENTS1. Introduction...................... 52. Definitions........................... 63. Stochastic processes.................. 74. Processes with independent increments...... 85. Sequential estimation for the Poisson process..... 126. Other processes with independent increments.......... 337. Efficiency for a given value of the parameter......... 398. Final remarks........................................... 43References................................................ 45 ...