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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...
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...
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 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.
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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