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Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives

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Author Info

  • Beresteanu, Arie

Abstract

Economic theory often provides us with qualitative information on the properties of the functions in a model but rarely indicates their explicit functional form. Among these properties one can find monotonicity, concavity and supermodularity, which involve restricting the sign of the regression's partial derivatives. This paper focuses on such restrictions and provides a sieve estimator based on nonparametric least squares. The estimator enjoys three main advantages: it can handle a variety of restrictions, separately or simultaneously; it is easy to implement; and its geometric interpretation highlights the small sample benefits from using prior information on the shape of the regression function. The last is achieved by evaluating the metric entropy of the space of shape-restricted functions. The small sample efficiency gains are approximated.

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Bibliographic Info

Paper provided by Duke University, Department of Economics in its series Working Papers with number 04-06.

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Length: 43 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:duk:dukeec:04-06

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Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
Phone: (919) 660-1800
Fax: (919) 684-8974
Web page: http://econ.duke.edu/

Related research

Keywords: Nonparametric regression; Shape restricted estimation; Sieve method; B-spline wavelets; Metric entropy;

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Cited by:
  1. Henderson, Daniel J. & Parmeter, Christopher F., 2009. "Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension," IZA Discussion Papers 4103, Institute for the Study of Labor (IZA).

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