Paul Doukhan
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View article: Pointwise Sharp Moderate Deviations for a Kernel Density Estimator
Pointwise Sharp Moderate Deviations for a Kernel Density Estimator Open
Let fn be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in Rd. With some mild conditions, we establish sharp moderate deviati…
View article: Inferring the parameters of Taylor's law in ecology
Inferring the parameters of Taylor's law in ecology Open
Taylor's power law (TL) or fluctuation scaling has been verified empirically for the abundances of many species, human and non-human, and in many other fields including physics, meteorology, computer science, and finance. TL asserts that t…
View article: Deviation inequalities for contractive infinite memory processes
Deviation inequalities for contractive infinite memory processes Open
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale d…
View article: Stationarity and ergodic properties for some observation-driven models in random environments
Stationarity and ergodic properties for some observation-driven models in random environments Open
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive …
View article: A Dynamic Taylor’s law
A Dynamic Taylor’s law Open
Taylor’s power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. The law has been shown to hold by empirical observations…
View article: Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality
Optimal Neighborhood Selection for AR-ARCH Random Fields with Application to Mortality Open
This article proposes an optimal and robust methodology for model selection. The model of interest is a parsimonious alternative framework for modeling the stochastic dynamics of mortality improvement rates introduced recently in the liter…
View article: Mixing properties of non-stationary INGARCH(1,1) processes
Mixing properties of non-stationary INGARCH(1,1) processes Open
We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary Poisson-GAR…
View article: Cramér moderate deviations for a supercritical Galton-Watson process
Cramér moderate deviations for a supercritical Galton-Watson process Open
Let $(Z_n)_{n\geq0}$ be a supercritical Galton-Watson process. The Lotka-Nagaev estimator $Z_{n+1}/Z_n$ is a common estimator for the offspring mean.In this paper, we establish some Cramér moderate deviation results for the Lotka-Nagaev es…
View article: Deviation inequalities for stochastic approximation by averaging
Deviation inequalities for stochastic approximation by averaging Open
We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz function…
View article: Mixing properties of Skellam-GARCH processes
Mixing properties of Skellam-GARCH processes Open
We consider integer-valued GARCH processes, where the count variable conditioned on past values of the count and state variables follows a so-called Skellam distribution. Using arguments for contractive Markov chains we prove that the proc…
View article: Optimal Neighborhoods Selection for AR-ARCH Random Fields with Application to Mortality
Optimal Neighborhoods Selection for AR-ARCH Random Fields with Application to Mortality Open
This article proposes an optimal and robust methodology for model selection. The model of interest is a parsimonious alternative framework for modeling the stochastic dynamics of mortality improvement rates introduced by Doukhan et al. (20…
View article: Spectral estimation for non-linear long range dependent discrete time trawl processes
Spectral estimation for non-linear long range dependent discrete time trawl processes Open
Discrete time trawl processes constitute a large class of time series parameterized by a trawl sequence (a j) j$\in$N and defined though a sequence of independent and identically distributed (i.i.d.) copies of a continuous time process ($γ…
View article: Multivariate count autoregression
Multivariate count autoregression Open
We are studying linear and log-linear models for multivariate count time series data with Poisson marginals. For studying the properties of such processes we develop a novel conceptual framework which is based on copulas. Earlier contribut…
View article: Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity
Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity Open
Extending the ideas of [7], this paper aims at providing a kernel based\nnon-parametric estimation of a new class of time varying AR(1) processes (Xt),\nwith local stationarity and periodic features (with a known period T), inducing\nthe d…
View article: Non-parametric estimation of time varying AR(1)--processes with local stationarity and periodicity
Non-parametric estimation of time varying AR(1)--processes with local stationarity and periodicity Open
Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the defi…
View article: Multivariate Count Autoregression
Multivariate Count Autoregression Open
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptua…
View article: Discrete-time trawl processes with long memory
Discrete-time trawl processes with long memory Open
We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent `seed' processes on shrinking intervals (`trawl heights'). Related trawl processes in continuo…
View article: Weak dependence of point processes and application to second-order statistics<sup>†</sup>
Weak dependence of point processes and application to second-order statistics<sup>†</sup> Open
We propose a general definition for weak dependence of point processes as an alternative to mixing definitions. We give examples of such weak dependent point processes for the families of Neyman Scott processes or Cox processes. For these …
View article: Phantom distribution functions for some stationary sequences
Phantom distribution functions for some stationary sequences Open
The notion of a phantom distribution function (phdf) was introduced by O'Brien (Ann. Probab. 15, 281–292 (1987)). We show that the existence of a phdf is a quite common phenomenon for stationary weakly dependent sequences. It is proved tha…
View article: Phantom distribution functions for some stationary sequences
Phantom distribution functions for some stationary sequences Open
The notion of a phantom distribution function (phdf) was introduced by O'Brien (1987). We show that the existence of a phdf is a quite common phenomenon for stationary weakly dependent sequences. It is proved that any $α$-mixing stationary…
View article: Empirical central limit theorem for cluster functionals without mixing
Empirical central limit theorem for cluster functionals without mixing Open
We prove central limit theorems (CLT) for empirical processes of extreme values cluster functionals as in Drees and Rootzén (2010). We use coupling properties enlightened for Dedecker \& Prieur's $τ-$dependence coefficients in order to imp…
View article: Empirical CLT for cluster functionals under weak dependence
Empirical CLT for cluster functionals under weak dependence Open
We prove empirical central limit theorems (CLT) for extreme values cluster functionals empirical processes in the sense of the tough paper Drees and Rootz\'en (2010). Contrary to those authors we dont restrict to $\beta$ - mixing samples. …