- Deconvolution for an atomic distribution: rates of convergence
- Journal of Nonparametric Statistics
- Volume | Issue number
- 23 | 4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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 rate-optimal in these cases.
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.