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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 157 (2010)
Issue (Month): 2 (August)
Pages: 362-374

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Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:362-374

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Nonparametric regression Cost and factor demand estimation Partial derivative data Curse of dimensionality Dimension reduction Rates of convergence Orthogonal series methods Cross-validation Smoothing parameter selection;

References

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  1. Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
  2. Eric Gautier & Yuichi Kitamura, 2008. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Working Papers 2008-15, Centre de Recherche en Economie et Statistique.
  3. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters, McMaster University Archive for the History of Economic Thought, in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1 McMaster University Archive for the History of Economic Thought.
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  5. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
  6. Jianqing Fan & Qiwei Yao, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
  7. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  8. Axel Munk & Nicolai Bissantz & Thorsten Wagner & Gudrun Freitag, 2005. "On difference-based variance estimation in nonparametric regression when the covariate is high dimensional," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 19-41.
  9. Hendriks, Harrie, 2003. "Application of fast spherical Fourier transform to density estimation," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 209-221, February.
  10. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521812832, 9.
  11. Jorgenson, Dale W., 1986. "Econometric methods for modeling producer behavior," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 31, pages 1841-1915 Elsevier.
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Cited by:
  1. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae 'Simon' Lee, 2014. "The identification power of smoothness assumptions in models with counterfactual outcomes," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP17/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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