Nonlinear wavelet density estimation under the Koziol–Green model

Abstract

In this work, nonlinear wavelet density estimation for censored data is introduced. We assume the Koziol–Green model of random censorship, under which the survival function of the censoring variable is a power of the survival function of interest. The L ₂ performance of the proposed estimate is investigated. Asymptotic expressions for the mean integrated squared error are provided, for both the smooth and unsmooth density cases.

Keywords:

• Proportional censorship
• Mean integrated squared error
• Wavelet

We are very grateful to Linyuan Li who provided us with a copy of his work Li (2002). As mentioned, some of the ideas for our proofs have been adapted from those in the referred work. Thanks also to a referee for comments and suggestions. This Work has been partially supported by the Grants PGIDIT02PXIA30003PR and BFM2002-03213.