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

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Let Xjr=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.
Twórcy
  • Department of Applied Mathematics, Warsaw University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776 Warszawa, Poland, konfur@wp.pl
Bibliografia
  • [1] D. W. K. Andrews and D. Pollard, An introduction to functional central limit theorems for dependent stochastic processes, Internat. Statist. Review 62 (1994), pp. 119-132.
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  • [9] H. L. Koul and D. Surgailis, Asymptotic expansion of M-estimators with long-memory errors, Ann. Statist. 25 (1997), pp. 818-850.
  • [10] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin 1991.
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  • [15] W. B. Wu, Central limit theorems for functionals of linear processes and their applications, Statist. Sinica 12 (2002), pp. 635-649.
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