Spectral Method for Deconvolving a Density
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.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2002|
|Date of revision:||2009|
|Publication status:||Published in Econometric Theory, vol. 27, June 2011, p. 546-581.|
|Contact details of provider:|| Postal: Manufacture des Tabacs, Aile Jean-Jacques Laffont, 21 Allée de Brienne, 31000 TOULOUSE|
Phone: +33 (0)5 61 12 85 89
Fax: + 33 (0)5 61 12 86 37
Web page: http://www.idei.fr/
More information through EDIRC
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.:
- Neumann, Michael H., 2007. "Deconvolution from panel data with unknown error distribution," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1955-1968, November.
- Eric Gautier & Yuichi Kitamura, 2013.
"Nonparametric Estimation in Random Coefficients Binary Choice Models,"
Econometric Society, vol. 81(2), pages 581-607, 03.
- Eric Gautier & Yuichi Kitamura, 2008. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Working Papers 2008-15, Centre de Recherche en Economie et Statistique.
- Eric Gautier & Yuichi Kitamura, 2011. "Nonparametric estimation in random coefficients binary choice models," Working Papers hal-00403939, HAL.
- Eric Gautier & Yuichi Kitamura, 2009. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Cowles Foundation Discussion Papers 1721, Cowles Foundation for Research in Economics, Yale University.
- Fabien Postel-Vinay & Jean-Marc Robin, 2002.
"Equilibrium Wage Dispersion with Worker and Employer Heterogeneity,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
- Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
- Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium wage dispersion with worker and employer heterogeneity," Sciences Po publications info:hdl:2441/dc0ckec3fcb, Sciences Po.
- Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Sciences Po publications info:hdl:2441/c8dmi8nm4pd, Sciences Po.
- Postel-Vinay, Fabien & Robin, Jean-Marc, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," CEPR Discussion Papers 3548, C.E.P.R. Discussion Papers.
- Ichimura, Hidehiko & Thompson, T. Scott, 1998.
"Maximum likelihood estimation of a binary choice model with random coefficients of unknown distribution,"
Journal of Econometrics,
Elsevier, vol. 86(2), pages 269-295, June.
- Ichimura, H. & Thompson, S., 1993. "Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distributions," Papers 268, Minnesota - Center for Economic Research.
- Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Oxford University Press, vol. 63(1), pages 145-168.
- Geweke, John, 1988. "Antithetic acceleration of Monte Carlo integration in Bayesian inference," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 73-89.
- Carrasco, Marine & Florens, Jean-Pierre, 2002. "Simulation-Based Method of Moments and Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 482-92, October.
- P. Groeneboom & G. Jongbloed, 2003. "Density estimation in the uniform deconvolution model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(1), pages 136-157.
- Raymond J. Carroll & Peter Hall, 2004. "Low order approximations in deconvolution and regression with errors in variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 31-46.
When requesting a correction, please mention this item's handle: RePEc:ide:wpaper:1038. 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: ()
If references are entirely missing, you can add them using this form.