Deconvolution for an atomic distribution
Bert van Es, Shota Gugushvili and Peter Spreij
Source: Electron. J. Statist. Volume 2 (2008), 265-297.
Abstract
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.
Primary Subjects: 62G07
Secondary Subjects: 62G20
Keywords: Asymptotic normality; atomic distribution; deconvolution; kernel density estimator
Full-text: Access granted (open access)
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1209565146
Digital Object Identifier: doi:10.1214/07-EJS121
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