Semi-recursive kernel conditional density estimators under random censorship and dependent data

In this work, we extend to the case of the strong mixing data the results of Khardani and Semmar. A kernel-type recursive estimator of the conditional density function is introduced. We study the properties of these estimators and compare them with Rosemblatt’s nonrecursive estimator. Then, a strong consistency rate as well as the asymptotic distribution of the estimator are established under an α-mixing condition. A simulation study is considered to show the performance of the proposed estimator.