We consider the problem of estimating a density and its derivatives for a sample of multiplicatively censored random variables. The purpose of this paper is to present an approach to this problem based on wavelets methods. Two different estimators are developed: a linear based on projections and a nonlinear using a term-by-term selection of the estimated wavelet coefficients. We explore their performances under the Lp-risk with p ≥ 1 and over a wide class of functions: the Besov balls. Fast rates of convergence are obtained. Finite sample properties of the estimation procedure are studied on a simulated data example.
|Number of pages||22|
|Journal||Revstat Statistical Journal|
|Publication status||Published - Nov 2013|
- Besov balls
- Density estimation
- Inverse problem
- Multiplicative censoring