Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

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

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
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.
  • Department of Applied Mathematics, Warsaw University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776 Warszawa, Poland,
  • [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.
  • [2] P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
  • [3] P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods, Springer, New York-Berlin-Heidelberg 1987.
  • [4] D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), pp. 1497-1504.
  • [5] K. Furmańczyk, Some remarks on the central limit theorem for functionals of linear processes under short-range dependence, Probab. Math. Statist. 27 (2007), pp. 235-245.
  • [6] L. Giraitis, Central limit theorem for functionals of linear process, Liet. Mat. Rink. 25 (1986), pp. 43-57.
  • [7] C. Ho and T. Hsing, On the asymptotic expansion of the empirical process of long memory moving averages, Ann. Statist. 24 (1996), pp. 992-1024.
  • [8] C. Ho and T. Hsing, Limit theorems for functional of moving averages, Ann. Probab. 25 (1997), pp. 1636-1669.
  • [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.
  • [11] V. V. Petrov, Limit Theorems of Probability Theory. Sequences of Independent Random Variables, Oxford University Press, Oxford 1995.
  • [12] A. N. Shiryaev, Probability, 2nd edition, Springer, 1996.
  • [13] W. F. Stout, Almost Sure Convergence, Wiley, New York 1974.
  • [14] A. Van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge 1998.
  • [15] W. B. Wu, Central limit theorems for functionals of linear processes and their applications, Statist. Sinica 12 (2002), pp. 635-649.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.