2007/09/30 by Bert van Es, Shota Gugushvili, Peter Spreij
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #msc:62G07 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/07-ejs121
published as Electronic Journal of Statistics 2008, Vol. 2, 265-297 · Published in at http://dx.doi.org/10.1214/07-EJS121 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2008/01/01 · arxiv created 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/01
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.