Rates of convergence for minimal distances in the central limit theorem under projective criteria.
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...
Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit. We also discuss...
On mean central limit theorems for stationary sequences
In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
On the functional central limit theorem for stationary processes
Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the Gaussian and the purely non-Gaussian parts of the infinitely divisible limit. We also discuss...
The empirical distribution function for dependent variables: asymptotic and nonasymptotic results in
Considering the centered empirical distribution function as a variable in , we derive non asymptotic upper bounds for the deviation of the -norms of as well as central limit theorems for the empirical process indexed by the elements of generalized Sobolev balls. These results are valid for a large class of dependent sequences, including non-mixing processes and some dynamical systems.
A quenched weak invariance principle
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
Estimation in autoregressive model with measurement error
Consider an autoregressive model with measurement error: we observe = + , where the unobserved is a stationary solution of the autoregressive equation = ( ) + . The regression function is known up to a finite dimensional parameter to be estimated. The distributions of and are unknown and ...
Moderate deviations for stationary sequences of bounded random variables
In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.
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