Lithuanian Mathematical Journal

, Volume 38, Issue 2, pp 131–143 | Cite as

Asymptotically minimax separation of two simple hypotheses

  • V. Kanišauskas


Renewal Process Simple Hypothesis Martingale Problem Elementary Calculus Stochastic Basis 
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  1. 1.
    Yu. N. Lin’kov,Asymptotic Methods of Statistics for Stochastic Processes [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
  2. 2.
    N. N. Chentsov,Statistical Decision Rules and Optimal Inference [in Russian], Nauka, Moscow (1972).Google Scholar
  3. 3.
    E. A. Morozova and N. N. Chentsov, Natural geometry of families of probability laws,Sovrem. Probl. Mat. Fund. Naprav.,83, 133–265 (1991).MATHMathSciNetGoogle Scholar
  4. 4.
    I. A. Ibragimov and R. Z. Khas’minskij,Asymptotic Theory of Estimation [in Russian], Nauka, Moscow (1979).Google Scholar
  5. 5.
    R. S. Ellis,Entropy, Large Deviations and Statistical Mechanics, Springer, Berlin (1985).Google Scholar
  6. 6.
    R. Sh. Liptser and A. N. Shiryaev,Martingale Theory [in Russian], Nauka, Moscow (1986).Google Scholar
  7. 7.
    Yu. M. Kabanov, R. Sh. Liptser, and A. N. Shiryaev, Absolute continuity and singularity of locally absolutely continuous probability distributions. I,Math. USSR Sb.,35, 631–680 (1979).MATHCrossRefGoogle Scholar
  8. 8.
    F. Liese and I. Vajda, Convex statistical distances,Teubner-Texte zur Mathematik,95 (1987).Google Scholar
  9. 9.
    B. Grigelionis, Hellinger integrals and Hellinger processes for solutions of martingale problems, in:Proc. V Vilnius Conference Probab. Theory and math. Statist., Vol. 1, VSP, Utrecht/Mokslas, Vilnius (1990), pp. 446–454.Google Scholar
  10. 10.
    B. Grigelionis, On Hellinger transforms for solutions of martingale problems, in:Stochastic Processes. A Festschrift in Honour of Gopinath Kallinapur, S. Cambanis et al. (Eds.), Springer-Verlag, New York (1993), pp. 107–116.Google Scholar
  11. 11.
    Yu. M. Kabanov, R. Sh. Liptser, and A. N. Shiryaev, Martingale methods in the theory of point processes, in:Proceedings of the School and Seminar on the Theory of Random Processes, Part 2, Inst. Fiz. Mat. Akad. Nauk Lit. SSR, Vilnius (1975), pp. 269–354.Google Scholar
  12. 12.
    D. W. Stroock,An Introduction to the Theory of Large Deviations, Springer, Berlin (1984).Google Scholar
  13. 13.
    J. D. Deuschel and D. W. Stroock,Large Deviations. Pure and Applied Mathematics, Academic Press (1989).Google Scholar
  14. 14.
    J. T. Cox and D. Griffeath, Large deviations for Poisson systems of independent random walks,Z. Wahrsch. verw. Geb.,66, 543–558 (1984).MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    R. Sh. Liptser and A. N. Shiryaev,Statistics of Random Processes [in Russian], Nauka, Moscow (1974).Google Scholar
  16. 16.
    E. Valkeila,A note on large deviation probabilities for the maximum likelihood estimator in filtered experiments, Preprint, University of Helsinki (1995).Google Scholar
  17. 17.
    V. Kanišauskas, Asymptotic estimation of parameters of multivariate point processes,Lith. Math. J.,37 (4), 352–363 (1997).Google Scholar

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© Plenum Publishing Corporation 1998

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  • V. Kanišauskas

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