Flexible Functional Forms Bernstein Polynomials

Pok Chak (), Neal Madras () and Barry Smith
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Pok Chak: York University, Canada
Neal Madras: Department of Mathematics and statistics, York University, Canada

Working Papers from York University, Department of Economics

Abstract: Motivated by the economic theory of cost functions, bivariate Bernstein polynomials are considered for approximating shape-restricted functions that are continuous, non-negative, monotone non-decreasing, concave, and homogeneous of degree one. We show the explicit rates of convergence of our approximating polynomials for general functions. We prove some interesting properties of bivariate Bernstein polynomials, including bimonotonicity for concave functions. Moreover, using the classical results, global approximations for shape-restricted functions can be achieved. We also note that concavity violation by the bivariate Bernstein polynomials occurs when the underlying true function ishomogeneous of degree one. However, this violation diminishes as indicces get large.

Keywords: bivariate Bernstein polynomials; rate of convergence; functional forms; flexibility; cost functions (search for similar items in EconPapers)
Pages: 36 pages
Date: 2001-11
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http://dept.econ.yorku.ca/research/workingPapers/w ... rs/approximation.pdf First version, 2001

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Persistent link: https://EconPapers.repec.org/RePEc:yca:wpaper:2001_02

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