An invariance principle for weakly dependent stationary general models

Details An invariance principle for weakly dependent stationary general models An invariance principle for weakly dependent stationary general models

2006-03-09

arxiv.org/abs/math/0603221v2

Probability and Mathematical Statistics, 2007, Vol. 1, pp 45 - 73

Mathematics

Statistics Theory

30 pages

Scientific paper

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak dependence assumptions used in Dedecker & Doukhan (2003). Here, if moments of order $>2$ exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan & Louhichi (1999) assumed the existence of moments with order $>4$. Besides the previously used $\eta$- and $\kappa$-weak dependence conditions, we introduce a weaker one, $\lambda$, which fits the Bernoulli shifts with dependent inputs.

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