Displaying similar documents to “Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes”

On-line nonparametric estimation.

Rafail Khasminskii (2004)

SORT

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A survey of some recent results on nonparametric on-line estimation is presented. The first result deals with an on-line estimation for a smooth signal S(t) in the classic 'signal plus Gaussian white noise' model. Then an analogous on-line estimator for the regression estimation problem with equidistant design is described and justified. Finally some preliminary results related to the on-line estimation for the diffusion observed process are described.

Unbiased risk estimation method for covariance estimation

Hélène Lescornel, Jean-Michel Loubes, Claudie Chabriac (2014)

ESAIM: Probability and Statistics

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We consider a model selection estimator of the covariance of a random process. Using the Unbiased Risk Estimation (U.R.E.) method, we build an estimator of the risk which allows to select an estimator in a collection of models. Then, we present an oracle inequality which ensures that the risk of the selected estimator is close to the risk of the oracle. Simulations show the efficiency of this methodology.

A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process

Romain Azaïs (2014)

ESAIM: Probability and Statistics

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In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a piecewise-deterministic Markov process, from only one observation of the path within a long time. In this framework, we do not observe a Markov chain with transition kernel of interest. Fortunately, one may write the transition density of interest as the ratio of the invariant distributions of two embedded chains of the process. Our method consists in estimating these...

Estimation of the transition density of a Markov chain

Mathieu Sart (2014)

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

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We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest...

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..............................................................................

Preface

Philippe Soulier (2002)

ESAIM: Probability and Statistics

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On the tail index estimation of an autoregressive Pareto process

Marta Ferreira (2013)

Discussiones Mathematicae Probability and Statistics

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In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision. ...

On invariant density estimation for ergodic diffusion processes.

Yuri A. Kutoyants (2004)

SORT

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We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator.

Nonparametric bivariate estimation for successive survival times.

Carles Serrat, Guadalupe Gómez (2007)

SORT

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Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for...

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...