Skip to main content
SpringerLink
Log in

The weak convergence of the likelihood ratio random fields for Markov observations

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bahadur, R. R. (1967). An optimal property of the likelihood ratio statistic,Proc. 5th Berkeley Symp. Math. Statist. Prob.,1, 13–36.

    MathSciNet  Google Scholar 

  2. Billingsley, P. (1961). The Lindeberg-Levy theorem for martingales,Proc. Amer. Math. Soc.,12, 788–792.

    Article  MathSciNet  Google Scholar 

  3. Billingsley, P. (1968).Convergence of Probability Measures, John Wiley & Sons, Inc., New York.

    MATH  Google Scholar 

  4. Davydov, Yu. A. (1973). Mixing conditions for Markov chains,Theory Prob. Appl.,18, 312–328.

    Article  Google Scholar 

  5. Doob, J. L. (1953).Stochastic Processes, John Wiley & Sons, Inc., New York.

    MATH  Google Scholar 

  6. Ibragimov, I. A. and Khas'minskii, R. Z. (1972). Asymptotic behavior of statistical estimators in the smooth case,Theory Prob. Appl.,17, 443–460.

    Google Scholar 

  7. Inagaki, N. and Ogata, Y. (1975). The weak convergence of likelihood ratio random fields and its applications,Ann. Inst. Statist. Math.,27, 391–419.

    MathSciNet  Google Scholar 

  8. Inagaki, N. and Ogata, Y. (1976). The weak convergence of the likelihood ratio random fields for Markov observations,Research Memorandum, No. 79, The Institute of Statistical Mathematics.

  9. LeCam, L. (1970). On the assumptions used to prove asymptotic normality of maximum likelihood estimates,Ann. Math. Statist.,41, 802–828.

    MathSciNet  Google Scholar 

  10. Ogata, Y. and Inagaki, N. (1976). The weak convergence of the likelihood ratio random fields for Markov observations II, (Asymptotic analysis for statistical Markovian models),Research Memorandum, No. 96, The Institute of Statistical Mathematics.

  11. Straf, M. L. (1970). Weak convergence of random processes with several parameters,Proc. 6th Berkeley Symp. Math. Statist. Prob.,2, 187–221.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Yosihiko Ogata & Nobuo Inagaki

Authors
  1. Yosihiko Ogata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nobuo Inagaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Ogata, Y., Inagaki, N. The weak convergence of the likelihood ratio random fields for Markov observations. Ann Inst Stat Math 29, 165–187 (1977). https://doi.org/10.1007/BF02532782

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02532782

Keywords

Search

Navigation