Open Access
2008 Deconvolution for an atomic distribution
Bert van Es, Shota Gugushvili, Peter Spreij
Electron. J. Statist. 2: 265-297 (2008). DOI: 10.1214/07-EJS121


Let X1,,Xn be i.i.d. observations, where Xi=Yi+σZi and Yi and Zi are independent. Assume that unobservable Y’s are distributed as a random variable UV, where U and V are independent, U has a Bernoulli distribution with probability of zero equal to p and V has a distribution function F with density f. Furthermore, let the random variables Zi have the standard normal distribution and let σ>0. Based on a sample X1,,Xn, we consider the problem of estimation of the density f and the probability p. We propose a kernel type deconvolution estimator for f and derive its asymptotic normality at a fixed point. A consistent estimator for p is given as well. Our results demonstrate that our estimator behaves very much like the kernel type deconvolution estimator in the classical deconvolution problem.


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Bert van Es. Shota Gugushvili. Peter Spreij. "Deconvolution for an atomic distribution." Electron. J. Statist. 2 265 - 297, 2008.


Published: 2008
First available in Project Euclid: 30 April 2008

zbMATH: 1135.62029
MathSciNet: MR2399196
Digital Object Identifier: 10.1214/07-EJS121

Primary: 62G07
Secondary: 62G20

Keywords: asymptotic normality , atomic distribution , Deconvolution , kernel density estimator

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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