On conditional independence, mixing, and association

Stochastic Analysis and Applications

Volumn 26, Issue 6, 2008, Pages 1274-1309

  Roussas, George G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Conditional association; Conditional characteristic function; Conditional covariance; Conditional independence of classes of events; Conditional independence of events; Conditional independence of random variables; Conditional mixing; Conditional variance

Indexed keywords

EID: 55249111087     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362990802405836     Document Type: Review

References (21)

1. Basawa, I.V., and Brockwell, P.J. 1984. Asymptotic conditional inference for regular nonergodic models with an application to autoregressive processes. Annals of Statistics 12:161-171.
2. Basu, A.K., and Bhattacharya, D. 1988. Local asymptotic mixed normality of log-likelihood based on stopping times. Calcutta Statistical Association Bulletin 37:143-159.
3. Bulinski, A., and Shashkin, A. 2007. Limit theorems for associated random fields and related systems. Advanced Series in Statistical Science and Applied Probability. Vol. 10. World Scientific, Singapore.
4. Chow, Y.S., Teicher, H. 1988. Probability Theory: Independence, Interchangeability, Martingales, 2nd ed. Springer-Verlag, New York.
5. Davis, R.B. 1985. Asymptotic inference when the amount of information is random. Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer. L. Le Cam, R.A. Olson, (eds.) Vol. II. Wodsworth, Monterey, CA, pp. 841-864.
6. Drossos, C. 2008. Personal communication.
7. Dubois, D., Goodman, I.R., and Calabrese, P.G. 1994. Editorial summary of articles for special issue of IEEE Transactions on Systems, Man, and Cybernetics. IEEE Transactions on Systems, Man, and Cybernetics 24(12):1665-1670.
8. Efron, B. 1975. Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics 3(6):1189-1242.
9. Greenwood, P.E., and Wefelmeyer, W. 1993. Asymptotic minimax results for stochastic process families with critical points. Stochastic Processes and Their Applications 44:107-116.
10. Jamison, B. 1974. Reciprocal processes. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 30:65-86.
11. Jeganathan, P. 1982. On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal. Sankhyā 44A:173-212.
12. Lehmann, E.L. 1966. Some concepts of dependence. Annals of Mathematics and Statistics 37:1137-1153.
13. Loève, M. 1963. Probability Theory. 3rd ed. Van Nostrand, Princeton, NJ.
14. Newman, C.M. 1980. Normal fluctuations and the FKG inequalities. Communications in Mathematical Physics 74:119-128.
15. Prakasa Rao, B.L.S. 2008. Conditional independence, conditional mixing and association. Annals of the Institute of Statistical Mathematics AISM, doi: 10.1007/S10463-007-0152-2.
16. Rényi, A. 1970. Foundations of Probability. Holden-Day, Inc., San Francisco.
17. Roussas, G.G. 1994. Asymptotic normality of random fields of positively or negatively associated processes. Journal of Multivariate Analysis 50:152-173.
18. Roussas, G.G. 1999. Positive and negative dependence with some statistical applications. In Asymptotics, Nonparametrics and Time Series, S. Ghosh, (ed.) Marcel Dekker, New York, pp. 757-788.
19. Roussas, G.G. 2005. An Introduction to Measure-Theoretic Probability. Elsevier Academic Press, Burlington, MA.
20. Roussas, G.G., and Ioannides, D. 1987. Moment inequalities for mixing sequences of random variables. Stochastic Analysis and Applications 5:61-120.
21. Van der Vaart, A.W. 1988. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge.