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Scientific Bulletin of Namangan State University

Abstract

In this paper the problem of estimation of unknown distribution density by using of orthonormal functions is considered.For certain systems of functions a validity of conditions of convergence to zero of expection of Hellinger’s distancy was shown.

First Page

53

Last Page

59

References

1. Abdushukurov A.A,,Abdulvoxidov A.L.,Muradov R.S. Otsenivanie blizosti proektsionnx otsenok plotnosti rasstoyaniem Xellingera.//Mejvuz. sb. “Statisticheskie metod otsenivaniya i proverki gipoteza”. Rossiya. Perm. Permskiy gosuniversitet. 2013. Vp. 25. str.11-20. 2. Beytmen G., Erdeyi A. Vsshie transtsendentne funktsii. M.Nauka. 1974.295 str. 3. Suetin P.K. Klassicheskie ortonormalne mnogochlen. M.Nauka. 1976. 327 str. 4. Xashimov Sh.A. Otsenka plotnosti veroyatnosti polinomami Lagerra. Ob sluchayne protsess i statisticheskie vvod. Tashkent. 1973. Vp 3. str .186-191. 5. Xashimov Sh.A. O statisticheskix yadernx otsenkax plotnostey raspredeleniy. Cb.Asimptoticheskie zadachi teorii veroyatnostey i matematicheskoy statistiki.Tashkent.1990.str 153-161. 6. Chentsov N.N. Otsenka neizvestnoy plotnosti raspredeleniya po nablyudeniyam. //Doklad AN SSSR.1962.t.147.№1.str.45-48. 7. Chentsov N.N. Statisticheskie reshayushie pravila i optimalne vvod. M. Nauka. 1972. 520.str. 8. Askey R., Wainger S. Mean convergence of expansion in Laguerre and Hermite series. //American J.Math. 1965.v.87.p.695-708. 9. Crain B. Estimation of distributions using orthogonal expansions. // Ann. Statist.1974.v.2.p.454-463. 10. Hall P. On the bootstrap and confidence intervals. //Ann. Statist. 1986.v.14.p.1431-1452. 11. Knonmal R., Tarter M. The estimation of probability densities and cumulatives by Fourier series methods. //. J.A.S.A.1968.V.63.P.925-952. 12. Schwarts S. Estimation of probability density by on orthogonal series. // Ann. Math. Stat. 1967. V. 38. p. 1261-1265. 13. Tien-Wen Chen. On the probability density estimation by Laguerre polinomials. // Tamkang J. Math. 1980. V. 11. p. 257-264. 14. Viollaz A. Non-parametric estimation of probability density functions based on orthogonal expansions. // Revista Math. 1989. V. 2. p. 41-82.

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