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Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives


  • Beresteanu, Arie


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.

Suggested Citation

  • Beresteanu, Arie, 2004. "Nonparametric Estimation of Regression Functions under Restrictions on Partieal Derivatives," Working Papers 04-06, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:04-06

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    Cited by:

    1. Eric Mbakop & Max Tabord-Meehan, 2016. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Papers 1609.03167,, revised Mar 2018.
    2. Henderson, Daniel J. & List, John A. & Millimet, Daniel L. & Parmeter, Christopher F. & Price, Michael K., 2012. "Empirical implementation of nonparametric first-price auction models," Journal of Econometrics, Elsevier, vol. 168(1), pages 17-28.
    3. 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).

    More about this item


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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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