Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T12:15:18.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Moment bounds for non-stationary dependent sequences

Published online by Cambridge University Press:  14 July 2016

Tae Yoon Kim
Tae Yoon Kim*
Affiliation:
Keimyung University
*
∗ Postal address: Department of Statistics, Keimyung University, Taegu 704–701, Korea.
Get access Rights & Permissions [Opens in a new window]

Abstract

We provide a unified approach for establishing even-moment bounds for partial sums for a class of weakly dependent random variables satisfying a stationarity condition. As applications, we discuss moment bounds for various types of mixing sequences. To obtain even-moment bounds, we use a ‘combinatorial argument' developed by Cox and Kim (1990).

Keywords

NON-STATIONARITYDEPENDENT RANDOM VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 731 - 742
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by the Non-Directed Fund, Korea Research Foundation, 1992.

References

Basu, A. K. (1985) On the rate of approximation in the central limit theorem for dependent random variables and random vectors. J. Multivariate Anal. 10, 565–573.CrossRefGoogle Scholar
Bradley, R. and Bryc, W. (1985) Multilinear forms and measures of dependence between random variables. J. Multivariate Anal. 16, 335–367.CrossRefGoogle Scholar
Butzer, P. L., Hahn, L. and Roeckerath, M. Th. (1983) Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces. J. Multivariate Anal. 13, 287–301.CrossRefGoogle Scholar
Cox, D. and Kim, T. Y. (1990) Moment bounds for sequence of strong mixing random variables useful in nonparametric regression. Technical Report 52, Department of Statistics, University of Illinois.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Doukhan, P., Leon, J. and Portal, F. (1984) Vitesse de convergence dans le théoreme centrale limite pour des variables aléatoires mélangeantes à valeurs un espace de Hilbert. C. R. Acad Sci. Paris Sér. I Math. 298, 305–308.Google Scholar
Glendinning, R. (1988) The rate of convergence in the central limit theorem for non-stationary dependent random vectors. J. Multivariate Anal. 26, 89–103.CrossRefGoogle Scholar
Ibragimov, I. A. (1962) Some limit theorems for stationary processes. Theory Prob. Appl. 7, 349–382.CrossRefGoogle Scholar
Kim, T. Y. (1993) A note on moment bounds for strong mixing sequences. Statist. Prob. Lett. 16, 163–168.CrossRefGoogle Scholar
Peligrad, M. (1987) The convergence of moments in the central limit theorem for ?-mixing sequences of random variables. Proc. Amer. Math. Soc. 101, 142–148.Google Scholar
Rhee, W. S. and Talagrand, M. (1981) On Berry-Essen type bounds for m-dependent random variables valued in certain Banach spaces. Z. Wahrscheinlichkeitsth. 58, 435–451.CrossRefGoogle Scholar
Roussas, G. and Ioannides, D. (1987) Moment inequalities for mixing sequences of random variables. Stoch. Anal. Appl. 5, 61–120.CrossRefGoogle Scholar
Yokoyama, R. Y. (1980) Moment bounds for stationary mixing sequences. Z. Wahrscheinlichkeitsth. 52, 45–57.CrossRefGoogle Scholar
Yoshihara, K. I. (1978) Moment inequalities for mixing sequences. Kodai Math. J. 1, 316–328.CrossRefGoogle Scholar