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Nonparametric least squares estimation in derivative families

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  • Hall, Peter
  • Yatchew, Adonis

Abstract

Cost function estimation often involves data on a function and a family of its derivatives. Such data can substantially improve convergence rates of nonparametric estimators. We propose series-type estimators which incorporate the various derivative data into a single nonparametric least-squares procedure. Convergence rates are obtained and it is shown that for low-dimensional cases, much of the beneficial impact is realized even if only data on ordinary first-order partials are available. In instances where root-n consistency is attained, smoothing parameters can often be chosen very easily, without resort to cross-validation. Simulations and an illustration of cost function estimation are included.

Suggested Citation

  • Hall, Peter & Yatchew, Adonis, 2010. "Nonparametric least squares estimation in derivative families," Journal of Econometrics, Elsevier, vol. 157(2), pages 362-374, August.
    • Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:362-374
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    2. Dimitri Dimitropoulos and Adonis Yatchew, 2017. "Is Productivity Growth in Electricity Distribution Negative? An Empirical Analysis Using Ontario Data," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).

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