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Flexible Functional Forms Bernstein Polynomials

Author

Listed:
  • Pok Man Chak

    (York University, Canada)

  • Neal Madras

    (Department of Mathematics and statistics, York University, Canada)

  • J. Barry Smith

    (York University, Canada)

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.

Suggested Citation

  • Pok Man Chak & Neal Madras & J. Barry Smith, 2001. "Flexible Functional Forms Bernstein Polynomials," Working Papers 2001_02, York University, Department of Economics.
    • Handle: RePEc:yca:wpaper:2001_02
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    File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/approximation.pdf
    File Function: First version, 2001
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