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Approximation of the Likelihood Ratio Statistics in the Model of Competing Risks Under Random Censoring from the Right

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In the competing risks model under random censoring from the right, an approximation of likelihood ratio statistics by a sequence of normally distributed stochastic integrals is established.

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References

  1. L. Le Cam, “Locally asymptotically normal families of distributions,” Unif. Calif. Publ. Statist., 3, 37–98 (1960).

    Google Scholar 

  2. J. Hajek, “Local asymptotic minimax and admissibility in estimation,” Proc. Sixth. Berkeley Symp. Math. Statist. Prob., 1, 175–194 (1972).

    MathSciNet  MATH  Google Scholar 

  3. I.A. Ibragimov and R. Z. Khasminskiy, Asymptotic Estimation Theory, Nauka, Moscow (1979).

    Google Scholar 

  4. J. Rusas, The Contiguity of Probability Measures, Mir, Moscow (1975).

    Google Scholar 

  5. P.K. Sen, “Weak convergence of progressively censored likelihood ratio statistics and its role in asymptotic theory of life testing,” Ann. Statist., 4, No. 6, 1247–1257 (1976).

    Article  MathSciNet  Google Scholar 

  6. J. Gardiner, “Local asymptotic normality for progressively censored likelihood ratio statistics and applications,” J. Multivar. Anal., 12, 230–247 (1982).

    Article  MathSciNet  Google Scholar 

  7. M. S. Tikhov, “Statistical analysis of grouped and censored observations,” in: Statistical Methods of Estimation and Hypothesis Testing, Perm. state. University, Perm (1978). pp. 122–137.

  8. A.A. Abdushukurov, “Approximation theorems for likelihood ratio statistics in the competing risk model I,” Uzbek Math. J., No. 1, 3–10 (1995).

  9. A.A. Abdushukurov, “Approximation theorems for likelihood ratio statistics in the competing risk model II,” Uzbek Math. J., No. 2, 3–11 (1996).

  10. A. A. Abdushukurov, Statistics of Incomplete Observations, University Press, Tashkent (2009).

  11. M.D. Burke, M. Csörgő, S. Csörgő, and P. Révész, “Approximations of the empirical process when parameters are estimated,” Ann. Probab., 7, No. 5, 790–810 (1978).

    MathSciNet  MATH  Google Scholar 

  12. N. Langberg, F. Proshan, and A. J. Quinzi, “Converting dependent models into independent ones, preserving essential features,” Ann. Probab., 6, 174–181 (1978).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. National University of Uzbekistan named after Mirzo Ulugbek, Faculty of Mechanics and Mathematics, Department of Probability Theory and Mathematical Statistics, Tashkent, Uzbekistan

    J. A. Bobojonov & N. S. Nurmuhamedova

Authors
  1. J. A. Bobojonov
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  2. N. S. Nurmuhamedova
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Correspondence to J. A. Bobojonov.

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Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 23, pp. 152–165, 2011

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Bobojonov, J.A., Nurmuhamedova, N.S. Approximation of the Likelihood Ratio Statistics in the Model of Competing Risks Under Random Censoring from the Right. J Math Sci 267, 122–131 (2022). https://doi.org/10.1007/s10958-022-06114-1

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  • DOI: https://doi.org/10.1007/s10958-022-06114-1

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