文章基本信息

标题：Bernstein-type approximations of smooth functions
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作者：Andrea Pallini
期刊名称：Statistica
印刷版ISSN：1973-2201
出版年度：2005
卷号：65
期号：2
页码：169-191
DOI：10.6092/issn.1973-2201/84
语种：English
出版社：Dep. of Statistical Sciences "Paolo Fortunati", Università di Bologna
摘要：The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution. The Bernstein-type approximations generalize the corresponding Bernstein polynomials, by considering definitions that depend on a convenient approximation coefficient in linear kernels. In the Bernstein-type approximations, we study the uniform convergence and the degree of approximation. The Bernstein-type estimators of smooth functions of population means are also proposed and studied.