In this article, we propose a non-parametric estimator for the probability density function of possibly censored data using a sequence of real polynomials. We have used the technique of likelihood cross-validation to obtain the smoothing parameter (degree of the polynomial) of the estimator. Asymptotic properties of the estimator are investigated. A simulation study is carried out to illustrate the accuracy of the estimator and compare the proposed estimator with kernel estimator. The proposed model is applied to a real data set.

polynomial density, smoothing parameter, likelihood cross-validation, censored mechanism.