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2 Furmańczyk K.

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Bounds for E׀Sn׀Q for subordinated linear processes with application to M-estimation

Furmańczyk K.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 1

129--141

Let Xj =Σ∞r=0 ArZj−r be a one-sided m-dimensional linear process, where (Zn) is a sequence of i.i.d. random vectors with zero mean and finite covariance matrix. The aim of this paper is to prove the moment inequalities of the form [formula] where G is a real function defined on Rm: The form of the constant C in (0.1) plays an important role in applications concerning the problems of M-estimation, especially the Ghosh representation.

Some remarks on the central limit theorem for functionals of linear processes under short-range dependence

Furmańczyk K.

Probability and Mathematical Statistics

2007

Vol. 27, Fasc. 2

235--245

In this paper we consider the central limit theorems for functionals G: Rm-> R of one-sided m-dimensional linear processes Xt=∑∞r=0 where Ar is a nonrandom matrix mxm and Zt’s are i.i.d. random vectors in Rm.