Bernstein-type approximations of smooth functions
AbstractThe 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.
How to Cite
Pallini, A. (2005). Bernstein-type approximations of smooth functions. Statistica, 65(2), 169–191. https://doi.org/10.6092/issn.1973-2201/84