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A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

Michael H. Neumann (2013)

ESAIM: Probability and Statistics

We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [Stoch. Proc. Appl. 84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of dependent Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics...

Analysis of an on-off intermittency system with adjustable state levels

Shi-Jian Cang, Zeng-Qiang Chen, Zhu Zhi Yuan (2008)

Kybernetika

We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...

Asymptotic normality of the kernel estimate for the Markovian transition operator

Samir Benaissa, Abbes Rabhi, Belaid Mechab (2011)

Applicationes Mathematicae

We build a kernel estimator of the Markovian transition operator as an endomorphism on L¹ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.

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...

Ecuaciones de la descomposición modal de procesos ARMA.

Juan José Egozcue Rubí, Eulàlia Griful Ponsati (1987)

Stochastica

Los procesos estocásticos estacionarios, autorregresivos y de medias móviles (ARMA), han sido estudiados en diversos ámbitos durante las dos últimas décadas (p.e. Brockwell-Davis, 1987), y se han utilizado con éxito en aplicaciones muy diversas.Uno de los aspectos al que parece que no se ha prestado demasiada atención es la descomposición aditiva de estos procesos, asociando cada componente a un polo de la función de transferencia del modelo ARMA. Esta descomposición aditiva, que llamaremos descomposición...

Efficient estimation of functionals of the spectral density of stationary Gaussian fields

Carenne Ludeña (2010)

ESAIM: Probability and Statistics

Minimax bounds for the risk function of estimators of functionals of the spectral density of Gaussian fields are obtained. This result is a generalization of a previous result of Khas'minskii and Ibragimov on Gaussian processes. Efficient estimators are then constructed for these functionals. In the case of linear functionals these estimators are given for all dimensions. For non-linear integral functionals, these estimators are constructed for the two and three dimensional problems.

Estimation of anisotropic gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2008)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional brownian field and prove that these processes admit...

Estimation of anisotropic Gaussian fields through Radon transform

Hermine Biermé, Frédéric Richard (2007)

ESAIM: Probability and Statistics

We estimate the anisotropic index of an anisotropic fractional Brownian field. For all directions, we give a convergent estimator of the value of the anisotropic index in this direction, based on generalized quadratic variations. We also prove a central limit theorem. First we present a result of identification that relies on the asymptotic behavior of the spectral density of a process. Then, we define Radon transforms of the anisotropic fractional Brownian field and prove that these processes...

Estimation of the spectral moment by means of the extrema.

Enrique M. Cabaña (1985)

Trabajos de Estadística e Investigación Operativa

An estimator of the standard deviation of the first derivative of a stationary Gaussian process with known variance and two continuous derivatives, based on the values of the relative maxima and minima, is proposed, and some of its properties are considered.

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