Bernstein-type approximations of smooth functions

Andrea Pallini
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Andrea Pallini: Dipartimento di Statistica e Matematica Applicata all’Economia - Università di Pisa

Statistica, 2005, vol. 65, issue 2, 169-191

Abstract: 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:bot:rivsta:v:65:y:2005:i:2:p:169-191

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