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Asymptotic distinction of counting processes

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Ukrainian Mathematical Journal Aims and scope

Abstract

A canonical representation is obtained for the logarithm of the likelihood ratio. Limit theorems describing its asymptotic behavior are proved. Using these theorems, we study the rate of decrease of the probability of an error of the second-kind in the Neyman-Pearson test.

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References

  1. Yu. N. Lin'kov,Asymptotic Methods of the Statistics of Random Processes [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  2. Yu. N. Lin'kov and Munir al Shakhf, “Asymptotic distinguishing of renewal processes,”Ukr. Mat. Zh.,44, No. 10, 1382–1388 (1992).

    Google Scholar 

  3. J. Jacod, “Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales,”Z. Wahrscheinlichkeitstheorie,31, No. 3, 235–253 (1975).

    Google Scholar 

  4. Yu. N. Lin'kov, “Asymptotic properties of the local density of measures for counting processes,” in:New Trends in Probability and Statistics, TYP/VSP, Vol. 4, Utrecht-Moscow (1993), pp. 73–97.

    Google Scholar 

  5. R. Sh. Liptser and A. N. Shiryaev,Theory of Martingales [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  6. R. Sh. Liptser, and A. N. Shiryaev, “The weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments,”Mat. Sb.,116, No. 3, 331–358 (1981).

    Google Scholar 

  7. Yu. N. Lin'kov,Asymptotic Distinguishing of Two Simple Statistical Hypotheses [in Russian], Preprint No. 86.45, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).

    Google Scholar 

  8. C. R. Rao,Linear Statistical Inference and its Applications, Wiley, New York (1965).

    Google Scholar 

  9. Yu. N. Lin'kov,Methods for Solving Asymptotic Problems of Testing Two Simple Statistical Hypotheses [in Russian], Preprint No. 89.05, Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk (1989).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    Yu. N. Lin'kov

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  1. Yu. N. Lin'kov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 972–979, July, 1993.

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Lin'kov, Y.N. Asymptotic distinction of counting processes. Ukr Math J 45, 1077–1085 (1993). https://doi.org/10.1007/BF01057454

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  • DOI: https://doi.org/10.1007/BF01057454

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