Skip to main content
Log in

Guaranteed statistical inference procedures (determination of the optimal sample size)

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

Literature cited

  1. A. A. Borovkov and A. I. Sakhanenko, “Rao-Cramer inequalities for Bayesian risk,” Teor. Veroyatn. Primen.,25, No. 1, 207–209 (1980).

    Google Scholar 

  2. M. V. Burnashev, “Sequential discrimination of hypotheses with control of observations,” Izv. Akad. Nauk SSSR, Ser. Math.,43, No. 6, 1203–1226 (1979).

    Google Scholar 

  3. A. Wald, Statistical Decision Functions, Wiley, New York (1950).

    Google Scholar 

  4. I. N. Volodin, “Estimating the necessary number of observations in statistical classification problems, I,” Teor. Veroyatn. Primen.,22, No. 2, 347–357 (1977).

    Google Scholar 

  5. I. N. Volodin, “Estimating the necessary number of observations in statistical classification problems, II,” Teor. Veroyatn. Primen.,22, No. 4, 749–765 (1977).

    Google Scholar 

  6. I. N. Volodin, “Estimating the mean of a normal distribution with guaranteed bounds on relative estimation error,” Zavod. Lab.,44, No. 1, 69–71 (1978).

    Google Scholar 

  7. I. N. Volodin, “Optimal sample size in statistical inference procedures,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 12, 33–45 (1978).

    Google Scholar 

  8. I. N. Volodin, “Lower bounds on the mean sample size and efficiency of statistical inference procedures,” Teor. Veroyatn. Primen.,24, No. 1, 119–129 (1979).

    Google Scholar 

  9. I. N. Volodin, “Lower bounds on the mean sample size in goodness-of-fit and homogeneity tests,” Teor. Veroyatn. Primen.,24, No. 3, 637–645 (1979).

    Google Scholar 

  10. I. N. Volodin, “Lower bounds on the mean sample size in invariance tests,” Teor. Veroyatn. Primen.,25, No. 2, 359–364 (1980).

    Google Scholar 

  11. I. N. Volodin, “Lower bounds on sufficient sample size in guaranteed equivariant estimation procedures,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 3, 14–17 (1982).

    Google Scholar 

  12. M. DeGroot, Optimal Statistical Decisions [Russian translation], Mir, Moscow (1974).

    Google Scholar 

  13. S. Zacks, The Theory of Statistical Inference [Russian translation], Mir, Moscow (1975).

    Google Scholar 

  14. Yu. Kruopis, “On comparison of many simple hypotheses,” Abstracts of papers at 2nd Vil'nius Conf. on Probability Theory and Mathematical Statistics [in Russian], Vol. 1, Vil'nius (1977), pp. 207–209.

    Google Scholar 

  15. S. Kullback, Information Theory and Statistics [Russian translation], Nauka, Moscow (1967).

    Google Scholar 

  16. E. Lehmann, Testing Statistical Hypotheses [Russian translation], Nauka, Moscow (1964).

    Google Scholar 

  17. Yu. V. Linnik, “On some general questions of sequential estimation theory,” Teor. Veroyatn. Primen.,27, No. 3, 596–597 (1972).

    Google Scholar 

  18. J. Neveu, Mathematical Foundations of Probability Theory [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  19. W. Feller, An Introduction to Probability Theory and Its Applications [Russian translation], Vol. 2, Mir, Moscow (1967).

    Google Scholar 

  20. A. N. Shiryaev, Statistical Sequential Analysis [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  21. G. W. Haggstrom, “Optimal stopping and experimental design,” Ann. Math. Stat.,37, No. 1, 7–29 (1966).

    Google Scholar 

  22. J. Neyman, “Two breakthroughs in the theory of statistical decision making,” Rev. Inst. Intern. Stat.,30, 11–27 (1962).

    Google Scholar 

  23. G. Simons, “Lower bounds for average sample number of sequential multihypothesis tests,” Ann. Math. Stat.,38, No. 5, 1343–1364 (1967).

    Google Scholar 

  24. Ch. Stein and A. Wald, “Sequential confidence intervals for the mean of a normal distribution with known variance,” Ann. Math. Stat.,18, 427–433 (1947).

    Google Scholar 

  25. J. Wolfowitz, “Asymptotic efficiency of the maximum likelihood estimator,” Teor. Veroy atn. Primen.,10, No. 2, 267–281 (1965).

    Google Scholar 

  26. M. B. Malyutov, “Lower bound for the mean size of a sequentially controlled sample,” Usp. Mat. Nauk,37, No. 2, 209–210 (1982).

    Google Scholar 

  27. M. B. Malyutov, “Lower bounds for the mean length of a sequentially planned experiment,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 19–41 (1983).

    Google Scholar 

  28. S. V. Simushkin, “Empirical d-posterior approach to the problem of guaranteed statistical inference,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 42–58 (1983).

    Google Scholar 

  29. I. N. Volodin and A. A. Novikov, “Asymptotic behavior of the necessary sample size for d-guaranteed discrimination of two close hypotheses,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 22, 59–66 (1983).

    Google Scholar 

  30. S. V. Simushkin, “Optimal sample size for d-guaranteed discrimination of hypotheses,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 47–52 (1982).

    Google Scholar 

Download references

Authors

Additional information

Translated from Issledovaniya po Prikladnoi Matematike, No. 10, pp. 13–53, 1984.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volodin, I.N. Guaranteed statistical inference procedures (determination of the optimal sample size). J Math Sci 44, 568–600 (1989). https://doi.org/10.1007/BF01095166

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01095166

Keywords

Navigation