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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...

A note on the properties of generalised separable spatial autoregressive process.

Shitan, Mahendran, Peiris, Shelton (2009)

Journal of Probability and Statistics

A unified approach to multivariable discrete-time filtering based on the Wiener theory

John F. Barrett, Thomas J. Moir (1987)

Kybernetika

Analyse spectrale et théorème de prédiction statistique de Wiener

Pierre Cartier (1960/1961)

Séminaire Bourbaki

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.