Consistent Estimation of Shape-Restricted Functions and Their Derivatives

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: 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.

Keywords: shape-restricted functions; bivariate Bernstein polynomials; flexible functional forms; sieve estimator; uniform consistency. (search for similar items in EconPapers)
JEL-codes: C13 C14 C15 C51 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2001-11
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http://dept.econ.yorku.ca/research/workingPapers/working_papers/estimation.pdf First version, 2001

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Persistent link: https://EconPapers.repec.org/RePEc:yca:wpaper:2001_03

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