An empirical central limit theorem for dependent sequences

Jerome Dedecker (1) , Clémentine Prieur (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse

We prove a central limit theorem for the d-dimensional distribution function of a class of stationary sequences. The conditions are expressed in terms of some coefficients which measure the dependence between a given σ-algebra and indicators of quadrants. These coefficients are weaker than the corresponding mixing coefficients, and can be computed in many situations. In particular, we show that they are well adapted to functions of mixing sequences, iterated random functions, and a class of dynamical systems.

Domaines: Probabilités [math.PR]

Jerome Dedecker, Clémentine Prieur. An empirical central limit theorem for dependent sequences. Stochastic Processes and their Applications, 2007, 117, pp.121-142. ⟨hal-00685975⟩