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Contents of PMS, Vol. 28, Fasc. 1,
pages 129 - 141
 

BOUNDS FOR Q E |Sn| FOR SUBORDINATED LINEAR PROCESSES WITH APPLICATION TO M -ESTIMATION

Konrad Furmańczyk

Abstract: Let X = sum o o A Z j r=0 r j- r be a one-sided m -dimensional linear process, where (Z ) n 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

E|S | Q < CnQ/2 n
(1)

for the sum
sum n ( ) Sn = G(Xj) - EG(Xj) , j=1
(2)

where G is a real function defined on Rm. The form of the constant C in (1) plays an important role in applications concerning the problems of M -estimation, especially the Ghosh representation.

2000 AMS Mathematics Subject Classification: Primary: 62M10, 62F12; Secondary: 60G35.

Key words and phrases: Linear process, empirical processes, time series, short-range dependence, M -estimation, the Ghosh representation.

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