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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.<\/jats:p>","DOI":"10.1017\/s026646661000040x","type":"journal-article","created":{"date-parts":[[2010,10,11]],"date-time":"2010-10-11T04:36:20Z","timestamp":1286771780000},"page":"546-581","source":"Crossref","is-referenced-by-count":34,"title":["A SPECTRAL METHOD FOR DECONVOLVING A DENSITY"],"prefix":"10.1017","volume":"27","author":[{"given":"Marine","family":"Carrasco","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Pierre","family":"Florens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,10,11]]},"reference":[{"key":"S026646661000040X_ref28","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS652"},{"key":"S026646661000040X_ref4","doi-asserted-by":"crossref","first-page":"5633","DOI":"10.1016\/S1573-4412(07)06077-1","volume-title":"The Handbook of Econometrics","volume":"6","author":"Carrasco","year":"2007"},{"key":"S026646661000040X_ref11","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1995.1008"},{"key":"S026646661000040X_ref34","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/24\/1\/015003"},{"key":"S026646661000040X_ref3","doi-asserted-by":"publisher","DOI":"10.1198\/073500102288618621"},{"key":"S026646661000040X_ref29","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2004.02056.x"},{"key":"S026646661000040X_ref20","volume-title":"Simulation-Based Econometric Methods","author":"Gourieroux","year":"1996"},{"key":"S026646661000040X_ref16","first-page":"97","article-title":"Asymptotic normality for deconvolution kernel density estimators","volume":"53","author":"Fan","year":"1991","journal-title":"Sankhya"},{"key":"S026646661000040X_ref46","first-page":"228","article-title":"Orthogonal series estimators of the prior distribution","volume":"43","author":"Walter","year":"1981","journal-title":"Sankhia: The Indian Journal of Statistics Series A"},{"key":"S026646661000040X_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(97)00117-6"},{"key":"S026646661000040X_ref38","doi-asserted-by":"crossref","first-page":"2033","DOI":"10.1214\/aos\/1017939249","article-title":"Adaptive wavelet estimator for nonparametric dendity deconvolution","volume":"27","author":"Pensky","year":"1999","journal-title":"Annals of Statistics"},{"key":"S026646661000040X_ref15","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348248"},{"key":"S026646661000040X_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2006.09.012"},{"key":"S026646661000040X_ref10","doi-asserted-by":"publisher","DOI":"10.2307\/3314852"},{"key":"S026646661000040X_ref13","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474005"},{"key":"S026646661000040X_ref18","doi-asserted-by":"crossref","unstructured":"Gautier E. & Kitamura Y. 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