 Author
 Year
 2011
 Title
 Deconvolution for an atomic distribution: rates of convergence
 Journal
 Journal of Nonparametric Statistics
 Volume  Issue number
 23  4
 Pages (fromto)
 10031029
 Document type
 Article
 Faculty
 Faculty of Science (FNWI)
 Institute
 Kortewegde Vries Institute for Mathematics (KdVI)
 Abstract

Let X 1, …, X n be i.i.d. copies of a random variable X=Y+Z, where X i =Y i +Z i , and Y i and Z i are independent and have the same distribution as Y and Z, respectively. Assume that the random variables Y i ’s are unobservable and that Y=AV, where A and V are independent, A has a Bernoulli distribution with probability of success equal to 1−p and V has a distribution function F with density f. Let the random variable Z have a known distribution with density k. Based on a sample X 1, …, X n , we consider the problem of nonparametric estimation of the density f and the probability p. Our estimators of f and p are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of f and p we show that our estimators are rateoptimal in these cases.
 URL
 go to publisher's site
 Language
 English
 Permalink
 http://hdl.handle.net/11245/1.358522
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