Advanced Search
MyIDEAS: Login to save this article or follow this journal

A Spectral Method For Deconvolving A Density

Contents:

Author Info

  • Carrasco, Marine
  • Florens, Jean-Pierre

Abstract

We propose a new estimator for the density of a random variable observed with an additive measurement error. This estimator is based on the spectral decomposition of the convolution operator, which is compact for an appropriate choice of reference spaces. The density is approximated by a sequence of orthonormal eigenfunctions of the convolution operator. The resulting estimator is shown to be consistent and asymptotically normal. While most estimation methods assume that the characteristic function (CF) of the error does not vanish, we relax this assumption and allow for isolated zeros. For instance, the CF of the uniform and symmetrically truncated normal distributions have isolated zeros. We show that, in the presence of zeros, the density is identified even though the convolution operator is not one-to-one. We propose two consistent estimators of the density. We apply our method to the estimation of the measurement error density of hourly income collected from survey data.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://journals.cambridge.org/abstract_S026646661000040X
File Function: link to article abstract page
Download Restriction: no

Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 27 (2011)
Issue (Month): 03 (June)
Pages: 546-581

as in new window
Handle: RePEc:cup:etheor:v:27:y:2011:i:03:p:546-581_00

Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:journals@cambridge.org

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics, EconWPA 9309001, EconWPA.
  2. Horowitz, Joel L & Markatou, Marianthi, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 63(1), pages 145-68, January.
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 in new window

Cited by:
  1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, Econometric Society, vol. 79(5), pages 1541-1565, 09.
  2. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011. "Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator," Econometric Theory, Cambridge University Press, vol. 27(03), pages 522-545, June.
  3. Manuel Arellano & Stéphane Bonhomme, 2009. "Identifying distributional characteristics in random coefficients panel data models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP22/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Yin, Zanhua & Gao, Wei & Tang, Man-Lai & Tian, Guo-Liang, 2013. "Estimation of nonparametric regression models with a mixture of Berkson and classical errors," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1151-1162.
  5. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 61-75.
  6. Stefan Hoderlein & Lars Nesheim & Anna Simoni, 2012. "Semiparametric estimation of random coefficients in structural economic models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP09/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
  8. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(04), pages 925-932, August.
  9. Susanne Schennach, 2013. "Convolution without independence," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP46/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:27:y:2011:i:03:p:546-581_00. 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: (Keith Waters).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.