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Communications in Statistics - Theory and Methods Volume 50, 2021 - Issue 17
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Original Articles

On estimating the Bernoulli regression function using Bernstein polynomials

P. K. BabiluaDepartment of Mathematics, Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
&
E. A. NadarayaDepartment of Mathematics, Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, Tbilisi, GeorgiaCorrespondence[email protected]
Pages 3928-3941 | Received 23 Mar 2019, Accepted 19 Dec 2019, Published online: 31 Jan 2020

References

  • Abbe, E. 1906. Über die Gesetrzmässigkeit in der Verteilung der Fehler bei Beobachtungsreihen. Werke, Bd. 2, 55–81. Jena.
  • Absava, R., and E. Nadaraya. 1999. Limit distribution of the mean square deviation of the Gasser-Muller nonparametric estimate of the regression function. Georgian Mathematical Journal 6 (6):501–16.
  • Aerts, M., and N. Veraverbeke. 1995. Bootstrapping a nonparametric polytomous regression model. Mathematical Methods of Statistics 4 (2):189–200.
  • Babilua, P. K., E. A. Nadaraya, and G. A. Sokhadze. 2015. On the square-integrable measure of the divergence of two kernel estimations of the Bernoulli regression functions. Ukrainian Mathematical Journal 67 (1):3–18; translation in Ukrainian Mathematical Journal 67 (2015), no. 1, 1–18. doi:https://doi.org/10.1007/s11253-015-1061-9.
  • Bhattacharya, P. K., and J. L. Gastwirth. 1999. Estimation of the odds-ratio in an observational study using bandwidth-matching. Journal of Nonparametric Statistics 11 (1–3):1–12. doi:https://doi.org/10.1080/10485259908832772.
  • Copas, J. B. 1983. Plotting p against x. Applied Statistics 32 (1):25–31. doi:https://doi.org/10.2307/2348040.
  • Cramér, H. 1946. Mathematical methods of statistics. Princeton mathematical series, Vol. 9. Princeton, NJ: Princeton University Press.
  • Efromovich, S. 1999. Nonparametric curve estimation. methods, theory, and applications. Springer Series in Statistics. New York: Springer-Verlag.
  • Feller, W. 1966. An introduction to probability theory and its applications. Vol. II. New York: John Wiley & Sons, Inc.
  • Leblanc, A. 2012. On estimating distribution functions using Bernstein polynomials. Annals of the Institute of Statistical Mathematics 64 (5):919–43. doi:https://doi.org/10.1007/s10463-011-0339-4.
  • Linnik, Y. V. 1958. The method of least squares and the foundations of the matematico-statistical theory of reduction of observations (Russian). Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit.
  • Lorentz, G. G. 1986. Bernstein Polynomials. 2nd ed. New York: Chelsea Publishing.
  • Mandzhgaladze, K. V. 1986. On some estimate of the distribution function and its moments (Russian). Soobscenija Akademii Nauk Gruzinskoj SSR 124:261–3.
  • Nadaraya, E., P. Babilua, and G. Sokhadze. 2013. About the nonparametric estimation of the Bernoulli regression. Communications in Statistics - Theory and Methods 42 (22):3989–4002. doi:https://doi.org/10.1080/03610926.2011.626550.
  • Okumura, H., and K. Naito. 2004. Weighted kernel estimators in nonparametric binomial regression. Journal of Nonparametric Statistics 16 (1-2):39–62. doi:https://doi.org/10.1080/10485250310001624828.
  • Shiryaev, A. N. 1989. Probability (Russian). Moscow: Nauka.

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