Abstract
We consider the linear inverse problem of recovering the density function for a sample of multiplicatively censored random variables. This is a problem arising in, e.g. estimation of waiting time distributions of renewal processes. The purpose of this paper is to present an approach to this problem using a singular value decomposition of the desired density. We establish conditions under which the rate of convergence of the mean integrated square error of the estimator is optimal. An empirical method for determining the order of expansion is suggested. Finite sample properties of the estimation procedure are studied on a simulated data example.
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