216
Views
27
CrossRef citations to date
0
Altmetric
Original Articles

On Conditional Independence, Mixing, and Association

Pages 1274-1309 | Received 27 Mar 2008, Accepted 28 Mar 2008, Published online: 29 Oct 2008

REFERENCES

  • 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 .
  • 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.
  • 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 .
  • Chow , Y.S. , Teicher , H. 1988 . Probability Theory: Independence, Interchangeability, Martingales , 2nd ed. , Springer-Verlag , New York .
  • 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 .
  • Drossos , C. 2008 . Personal communication .
  • 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 .
  • Efron , B. 1975 . Defining the curvature of a statistical problem (with applications to second order efficiency) . Annals of Statistics 3 ( 6 ): 1189 – 1242 .
  • 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 .
  • Jamison , B. 1974 . Reciprocal processes . Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 30 : 65 – 86 .
  • Jeganathan , P. 1982 . On the asymptotic theory of estimation when the limit of the log-likelihood ratios is mixed normal . Sankhya 44A : 173 – 212 .
  • Lehmann , E.L. 1966 . Some concepts of dependence . Annals of Mathematics and Statistics 37 : 1137 – 1153 .
  • Loève , M. 1963 . Probability Theory. , 3rd ed. Van Nostrand , Princeton, NJ .
  • Newman , C.M. 1980 . Normal fluctuations and the FKG inequalities . Communications in Mathematical Physics 74 : 119 – 128 .
  • 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 .
  • Rényi , A. 1970 . Foundations of Probability . Holden-Day, Inc ., San Francisco .
  • Roussas , G.G. 1994 . Asymptotic normality of random fields of positively or negatively associated processes . Journal of Multivariate Analysis 50 : 152 – 173 .
  • 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 .
  • Roussas , G.G. 2005 . An Introduction to Measure-Theoretic Probability . Elsevier Academic Press , Burlington, MA .
  • Roussas , G.G. , and Ioannides , D. 1987 . Moment inequalities for mixing sequences of random variables . Stochastic Analysis and Applications 5 : 61 – 120 .
  • Van der Vaart , A.W. 1988 . Asymptotic Statistics . Cambridge Series in Statistical and Probabilistic Mathematics . Cambridge University Press , Cambridge .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.