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Bernstein-type approximations of smooth functions

Author

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  • Andrea Pallini

    (Dipartimento di Statistica e Matematica Applicata all’Economia - Università di Pisa)

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.

Suggested Citation

  • Andrea Pallini, 2005. "Bernstein-type approximations of smooth functions," Statistica, Department of Statistics, University of Bologna, vol. 65(2), pages 169-191.
    • Handle: RePEc:bot:rivsta:v:65:y:2005:i:2:p:169-191
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