Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-17

May 1999

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 or orthonormal based series expansion of the desired density. We establish conditions under which the mean integrated square error of the estimator converges to zero for increasing sample size. An empirical method for determining the order of expansion is suggested. Finite sample properties of the estimation procedure are studied on an artificial data example.

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