A Spectral Method For Deconvolving A Density
AbstractWe 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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 27 (2011)
Issue (Month): 03 (June)
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- Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics, EconWPA 9309001, EconWPA.
- 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.
- 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.
- Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers, Centre de Recherche en Economie et Statistique 2000-17, Centre de Recherche en Economie et Statistique.
- Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
- DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Ã‰ric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-05, Universite de Montreal, Departement de sciences economiques.
- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2011.
"Convergence Rates For Ill-Posed Inverse Problems With An Unknown Operator,"
Cambridge University Press, vol. 27(03), pages 522-545, June.
- Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2009. "Convergence Rates for III-Posed Inverse Problems with an Unknown Operator," TSE Working Papers 09-030, Toulouse School of Economics (TSE).
- Manuel Arellano & StÃ©phane 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.
- Manuel Arellano & StÃ©phane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 987-1020.
- Manuel Arellano & StÃ©phane Bonhomme, 2009. "Identifying Distributional Characteristics In Random Coefficients Panel Data Models," Working Papers, CEMFI wp2009_0904, CEMFI.
- 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.
- Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 167(1), pages 61-75.
- 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.
- 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.
- Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(04), pages 925-932, August.
- 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.
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