Multiplicative Censoring: Estimation of a Density and its Derivatives under the Lp-Risk
Keywords:density estimation, multiplicative censoring, inverse problem, wavelets, Besov balls, Lp-risk
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.
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