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Consistent Estimation of Shape-Restricted Functions and Their Derivatives

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

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.

Suggested Citation

  • Pok Man Chak & Neal Madras & J. Barry Smith, 2001. "Consistent Estimation of Shape-Restricted Functions and Their Derivatives," Working Papers 2001_03, York University, Department of Economics.
    • Handle: RePEc:yca:wpaper:2001_03
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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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    More about this item

    Keywords

    shape-restricted functions; bivariate Bernstein polynomials; flexible functional forms; sieve estimator; uniform consistency.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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