Elizbar Nadaraya

Corresponding Member of Georgian Academy of Sciences (Mathematics)

Family name, name:	Nadaraya Elizbar
Date and place of birth:	April 17, 1936, Khobi, Georgia
Post-graduate study:	Steklov Mathematical Institute of USSR Academy of Science, Moscow
Scientific title:	Professor, the probability theory and mathematical statistics chair of Tbilisi State University (1983).
Academic degrees:	Candidate of Physical and Mathematical Sciences (1964, Moscow Steklov Mathematical Institute), Doctor of Physical and Mathematical Sciences (1981, Tashkent Romanovski Mathematical Institute
Main research areas:	Probability theory and mathematical statistics
Pedagogical work and scientific-organization activity:	Researcher at Computational Center of Georgian Academy of Sciences (1964—1966); Researcher and later head of the probability theory and mathematical statistics department of I. Vekua Applied Mathematics Institute under Tbilisi State University (1966—1973); Head of the probability theory and mathematical statistics department of the Economics and Law Institute of Georgian Academy of Sciences (1973—1978); Docent, professor (1978—1986), head (1986 – presently) of the probability theory and mathematical statistics chair of Tbilisi State University.
Awards:	I. Vekua Prize of Georgian Academy of Sciences in Mathematics (1990).
Address, telephone:	2 University Str., 380043 Tbilisi, Georgia Tel.: 30-41-45; 899-57-05-55

Published Works

Monographs

1. Nonparametric estimation of probability densities and regression curves. (Russian) Tbilisi State University Press, 1983.

2. Nonparametric estimation of probability densities and regression curves. Kluwer Academic Publishers (1989).

Main Research Papers

1. Some new estimates for distribution functions. Theory Prob. and Appl. (1964), 9, 3, 497—500.

2. On estimating regression. Theory Prob.and Appl. (1964), 9, 141—142.

3. On non-parametric estimates of density functions and regression curves. Theory Prob. and Appl. (1965), 10, 1, 186—191.

4. Nonparametric estimation of regression curves. (Russian) Transact. Comp. Center Acad. Sci. Georgian SSR (1965), 5, 1, 56—68.

5. Remarks on nonparametric estimates for density functions and regression curves. Theory Prob. and Appl. (1970), 15, 1, 134—137.

6. On the construction of confidence regions for probability densities. (Russian) Bull. Acad. Sci. Georgian SSR (1970), 59, 1, 33—36.

7. On convergence in the L₂ norm of probability density estimates. Theory Prob. and Appl. (1973), 18, 808—811.

8. Some limit theorems related to nonparametric estimates of regression functions. (Russian) Bull. Acad. Sci. Georgian SSR (1973), 71, 1, 56—60.

9. On the mean square error of some nonparametric estimators of probability density. (Russian) Theory Prob. and Math. Statistics (1974), 10, 116-129.

10. Limiting distribution of quadratic deviation of nonparametric regression estimators. (Russian) Bull. Acad. Sci. Georgian SSR (1974), 74, 1, 33—36.

11. On the integral mean square error of some nonparametric estimates for the density function. Theory Prob. and Appl. (1974), 19, 1, 133—142.

12. On the construction of confidence regions for probability densities. (Russian) Transact. I. Vekua Inst. Appl. Math., Tbilisi State University. Press, (1975), 183—204.

13. Limiting distribution of quadratic deviation of two nonparametric density estimators. (Russian) Bull. Acad. Sci. Georgian SSR (1975), 78, 1, 25—28.

14. On the nonparametric estimator of Bayesian risk in the classification problem. (Russian) Bull. Acad. Sci. Georgian SSR (1976), 82, 2, 277-280.

15. On the quadratic measure of deviation of projection estimates of a distribution density. Theory Prob. and Appl. (1976), 21, 4, 843—850.

16. Remarks on the convergence of kernel-type density estimators in variation. (Russian) Bull. Acad. Sci. Georgian SSR (1980), 97, 3, 577—580.

17. On some tests based on kernel type density estimators. (Russian) Bull. Acad. Sci. Georgian SSR (1980), 99, 1, 37—40.

18. A limit distribution of the square error deviation on nonparametric estimators of the regression function. Z. Wahrscheinlichklitstheorie Verw. Gebiete (1983), 64, 37—48.

19. On maximal deviation of the kernel type nonparametric density estimates in some degenerate cases. Math. Operations forsch. Statist., Ser. Statist. (1980), 11, 4, 483—497.

20. Application of the martingale central limit theorem for a study of the limiting distribution of quadratic deviation of the kernel-type density estimators. (Russian) Bull. Acad. Sci. Georgian SSR (1984), 113, 2, 253—256.

21. On the limiting distribution of quadratic deviation for a generalization class of kernel density estimators. (Russian) Theory Prob. and Appl. (1992), 37, 413—421.

22. On the limiting distribution of quadratic deviation for a wide class of probability density estimators. (Russian) Proc. A. Razmadze Math. Inst. (1989), 92, 164—185 (in coauthorship with R. Absava).

23. Limit distribution of the integrated square error of trigonometric series regression estimators. Proc.Georgian Acad. Sci. Mathematics 1 (1993), 2, 221—237.

24. Limit distribution of the mean square deviation of the Gasser-Müller nonparametric estimate of the regression function. Georgian Math. Journal (1999), 6, 6, 501—516 (in coauthorship with R. Absava).

25. On quadratic measure of deviation of nonparametric estimation of the Gasser-Müller regression function. Proc. A. Razmadze Math. Inst. (2000), 122, 1—14 (in coauthorship with R. Absava).

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