IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v157y2010i2p362-374.html
   My bibliography  Save this article

Nonparametric least squares estimation in derivative families

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00081-3
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters,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.
    2. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.
    3. 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.
    4. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, March.
    5. repec:taf:gnstxx:v:21:y:2009:i:5:p:611-628 is not listed on IDEAS
    6. Florens, Jean-Pierre & Ivaldi, Marc & Larribeau, Sophie, 1996. "Sobolev Estimation of Approximate Regressions," Econometric Theory, Cambridge University Press, vol. 12(05), pages 753-772, December.
    7. Jorgenson, Dale W., 1986. "Econometric methods for modeling producer behavior," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 31, pages 1841-1915 Elsevier.
    8. Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
    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 9780521012263.
    11. Fan, Jianqing & Yao, Qiwei, 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.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2014. "The identification power of smoothness assumptions in models with counterfactual outcomes," CeMMAP working papers CWP17/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:157:y:2010:i:2:p:362-374. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.