Skip to main content
Log in

Determination of the Smoothing Parameter of an Unbiased Estimator of the Efficiency Function in the Dose-Effect Relationships

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

An algorithm of adaptive determination of the bandwidth is considered for unbiased estimators of the efficiency function in the dose-effect relationship under a fixed experimental design in the case of direct measurements. Optimality of the proposed algorithm is proved.

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.

Similar content being viewed by others

References

  1. S.V. Krishtopenko, M. S. Tikhov, and E.B. Popova, Dose–Effect, Meditsina, Moscow (2008).

  2. S.V. Krishtopenko and M. S. Tikhov, Toxicometry of Effective Doses, State University of Nizhny Novgorod Publishers, Nizhny Novgorod (1997).

    Google Scholar 

  3. S.V. Krishtopenko, M. S. Tikhov, and E.B. Popova, Paradoxical Toxicity, State Medical Academy of Nizhny Novgorod Publishers, Nizhny Novgorod (2001).

    Google Scholar 

  4. M. S. Tikhov, “Statistical estimation based on interval censored data,” in: Parametric and Semipara-metric Models with Applications to Reliability, Survival Analysis and Quality of Life, M. S. Nikulin, N. Balakrishnan, M. Mesbah, and N. Limnios (eds.), Birkhauser, Boston (2004), pp. 209–215.

    Google Scholar 

  5. M. S. Tikhov, D. S. Krishtopenko, and M.V. Yaroschuk, “Estimation of distributions under doseeffect dependence with fixed experiment plan,” J. Math. Sci., 220, 753–762 (2017).

    Article  MathSciNet  Google Scholar 

  6. M. S. Tikhov and D. S. Krishtopenko, “Asymptotic distributions for integrated square error at the fixed plan of experiment,” in: 9th International Vilnius Conference on Probability Theory and Math-ematical Statistics: Abstract of Communications, Vilnius (2006), p. 312.

  7. M. S. Tikhov and D. S. Krishtopenko, “Asymptotic normality of the integrated square error at the random plan of experiment with dose measurement errors,” in: Proceedings of the 6th International Conference Reliability and Statistics in Transportation and Communication, Riga (2006). pp. 374–375.

  8. M. S. Tikhov and D. S. Krishtopenko, “Asymptotic normality of the integrated square error of distribution function estimators in dependence dose-response from indirect observations,” in: XIIth International Conference on Applied Stochastic Models and Data Analysis (ASMDA), Chania, Crete (2007).

  9. W. Hardle, P. Hall, and J. S. Marron, “How far are automatically chosen regression smoothing parameters from their optimum?” J. Amer. Statist. Assoc., 83, No. 401, 86–93 (1988).

    MathSciNet  MATH  Google Scholar 

  10. J. Rice, “Bandwidth choice for nonparametric regression,” Ann. Statist., 12, No. 4, 1215–1230 (1984).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. S. Tikhov.

Additional information

Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, Vol. 22, pp. 85–95, 2010

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tikhov, M.S., Krishtopenko, D.S. Determination of the Smoothing Parameter of an Unbiased Estimator of the Efficiency Function in the Dose-Effect Relationships. J Math Sci 267, 36–42 (2022). https://doi.org/10.1007/s10958-022-06105-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-06105-2

Navigation