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Dependent Lindeberg central limit theorem and some applications

Jean-Marc Bardet, Paul Doukhan, Gabriel Lang, Nicolas Ragache (2008)

ESAIM: Probability and Statistics

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...

Determination of phase-space reconstruction parameters of chaotic time series

Wei-Dong Cai, Yi-Qing Qin, Bing Ru Yang (2008)

Kybernetika

A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period N, a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N,r,t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a...

Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

S. Valère Bitseki Penda, Hacène Djellout (2014)

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

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general p th-order asymmetric bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales.

Discrete sampling of an integrated diffusion process and parameter estimation of the diffusion coefficient

Arnaud Gloter (2010)

ESAIM: Probability and Statistics

Let (Xt) be a diffusion on the interval (l,r) and Δn a sequence of positive numbers tending to zero. We define Ji as the integral between iΔn and (i + 1)Δn of Xs. We give an approximation of the law of (J0,...,Jn-1) by means of a Euler scheme expansion for the process (Ji). In some special cases, an approximation by an explicit Gaussian ARMA(1,1) process is obtained. When Δn = n-1 we deduce from this expansion estimators of the diffusion coefficient of X based on (Ji). These estimators are shown...

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