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Consistent Estimation of Shape-Restricted Functions and Their Derivatives

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Author Info

  • Pok Man Chak

    ()
    (York University, Canada)

  • Neal Madras

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

  • J. Barry Smith

    ()
    (York University, Canada)

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    Abstract

    We examine the estimation problem for shape-restricted functions that are continuous, non-negative, monotone non-decreasing, and strictly concave. A sieve estimator based on bivariate Bernstein polynomials is proposed. This estimator is drawn from a sieve, a set of shape-restricted Bernstein polynomials, which grows with the sample size in such a way that it becomes dense in the set of shape-restricted functions. Under some mild conditions, we show that this sieve estimator of the true function and the estimators of its first and second derivatives are uniformly consisten. THe estimators of elasticities of substitution are uniformly consistent as well.

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    File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/estimation.pdf
    File Function: First version, 2001
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    Bibliographic Info

    Paper provided by York University, Department of Economics in its series Working Papers with number 2001_03.

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    Length: 36 pages
    Date of creation: Nov 2001
    Date of revision:
    Handle: RePEc:yca:wpaper:2001_03

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    Related research

    Keywords: shape-restricted functions; bivariate Bernstein polynomials; flexible functional forms; sieve estimator; uniform consistency.;

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