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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 294, Pages 127–138 (Mi znsl1690)  
Estimation of probability characteristics by generalized bernstein polynomials

J. W. Leea, G. L. Shevlyakovb, N. O. Vilshevskiib

a Kumoh Naitonal University of Technology
b State Technological Institute of St. Petersburg
Full-text PDF (160 kB)
Abstract: Approximations based on the Bernstein polynomials are used for smoothing a sample quantile function and estimating the underlying distribution and its characteristics. The generalized Bernstein-type polynomials are introduced to reduce the bias of estimation under various types of distributions including finite distributions. The asymptotic behavior of the expectations of these estimators is studied.
Received: 10.07.2002
English version:
Journal of Mathematical Sciences (New York), 2005, Volume 127, Issue 1, Pages 1745–1751
DOI: https://doi.org/10.1007/s10958-005-0135-x
Bibliographic databases:
UDC: 519.21
Language: English
Citation: J. W. Lee, G. L. Shevlyakov, N. O. Vilshevskii, “Estimation of probability characteristics by generalized bernstein polynomials”, Probability and statistics. Part 5, Zap. Nauchn. Sem. POMI, 294, POMI, St. Petersburg, 2002, 127–138; J. Math. Sci. (N. Y.), 127:1 (2005), 1745–1751
Citation in format AMSBIB
\Bibitem{LeeSheVil02}
\by J.~W.~Lee, G.~L.~Shevlyakov, N.~O.~Vilshevskii
\paper Estimation of probability characteristics by generalized bernstein polynomials
\inbook Probability and statistics. Part~5
\serial Zap. Nauchn. Sem. POMI
\yr 2002
\vol 294
\pages 127--138
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1690}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1976751}
\zmath{https://zbmath.org/?q=an:1072.62024}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 127
\issue 1
\pages 1745--1751
\crossref{https://doi.org/10.1007/s10958-005-0135-x}
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