Variation convergence for Bernstein polynomials
نویسندگان
چکیده
منابع مشابه
Convergence Rates for Density Estimation with Bernstein Polynomials
Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexible model. The class of Bernstein densities is a much smaller subclass of the beta mixtures defined by Bernstein polynomials, which can approximate any continuous density. A Bernstein polynomial prior i...
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The convergence properties of q-Bernstein polynomials are investigated. When q > 1 is fixed the generalized Bernstein polynomials Bnf of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then Bnf → f if and only if f is linear. The iterates of Bnf are also considered. It is shown that B n f c...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0226259-3