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On the Decrease in Dependence with Lag for Stationary Markov Chains

Published online by Cambridge University Press:  27 July 2009

Zhaoben Fang ,
Taizhong Hu  and
Harry Joe
Zhaoben Fang
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Taizhong Hu
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Harry Joe
Affiliation:
Department of Statistics, University of British Columbia, Vancouver, British Columbia, CanadaV6T 1Z2
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Abstract

Results and conditions that quantify the decrease in dependence with lag for stationary Markov chains are obtained. Notions of dependence that are used are the concordance or positive quadrant dependence ordering, measures of dependence based on ψ-divergences such as the relative entropy measure of dependence, and the Goodman-Kruskal measure of association. The general results are mainly for first-order Markov chains, but there are also some results for higher order Markov chains.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 3 , July 1994 , pp. 385 - 401
Copyright
Copyright © Cambridge University Press 1994

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References

1.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.Google Scholar
2.Box, G.E.P. & Jenkins, G.M. (1976). Time series, forecasting and control, rev. ed. San Francisco: Holden-Day.Google Scholar
3.Cover, T.M. & Thomas, J.A. (1991). Elements of information theory. New York: Wiley.Google Scholar
4.Csiszar, I. (1972). A class of measures of informativity of observation channels. Periodica Mathematica Hungarica 2: 191–213.CrossRefGoogle Scholar
5.Esary, J.E., Proschan, F., & Walkup, D.W. (1967). Association of random variables with applications. Annals of Mathematical Statistics 44: 1466–1474.CrossRefGoogle Scholar
6.Hoeffding, W. (1940). A class of statistics with asymptotically normal distributions. Annals of Mathematical Statistics 19: 293–375.CrossRefGoogle Scholar
7.Joe, H. (1989). Relative entropy measures of multivariate dependence. Journal of the American Statistical Association 84: 157–164.CrossRefGoogle Scholar
8.Joe, H. (1990). Majorization and divergence. Journal of Mathematical Analysis and Applications 148: 287–305.CrossRefGoogle Scholar
9.Joe, H. (1990). Multivariate concordance. Journal of Multivariate Analysis 35: 12–30.CrossRefGoogle Scholar
10.Joe, H. (1993). Parametric families of multivariate distributions with given margins. Journal of Multivariate Analysis 46: 262–282.CrossRefGoogle Scholar
11.Lehmann, E.L. (1966). Some concepts of dependence. Annals of Mathematical Statistics 37: 1137–1153.CrossRefGoogle Scholar
12.Marshall, A.W. & Olkin, I. (1988). Families of multivariate distributions. Journal of the American Statistical Association 83: 834–841.CrossRefGoogle Scholar
13.Priestley, M.B. (1981). Spectral analysis and time series, Vol. 1: Univariate series. New York: Academic.Google Scholar
14.Tchen, A. (1980). Inequalities for distributions with given marginals. Annals of Probability 8: 814–827.CrossRefGoogle Scholar
15.Yaganimoto, T. & Okamoto, M. (1969). Partial orderings of permutations and montonicity of a rank correlation statistic. Annals of the Institute of Statistical Mathematics 21: 489–505.CrossRefGoogle Scholar