Density estimation with laguerre series and censored samples

摘要

In this paper we investigate the nonparametric density estimation by means of the orthonormal system of the Laguerre series on the positive half line. We work with stochastically right censored samples, discuss the asymptotic convergence behaviour in this case and give convergence rates either of the mean integrated square error and the mean square error. With an extra assumption on the distribution functions we are in position to obtain the same convergence order as in the case of uncensored samples.