Density and Risk Function of the Circular Kernel Study

Abstract

This article is based on the works of [1], [2] and [3] on the estimation of the survival function and the function of risk in independent cases and identically distributed with and without censorship from which we established the bias and variance of the density of the circular kernel. In addition, we determined the optimal window b ∗ n of this estimator after having first established the mean square error (MSE) and mean integrated squared error (MISE) which are necessary conditions for obtaining the optimal window. Finally, we have established the asymptotic expression of the bias of the risk function of the circular kernel estimator