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

Abstract

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.

Keywords:

• Asymptotic normality
• censored data
• conditional density
• mixing sequences
• recursive kernel estimators
• survival data
• strong consistency

AMS Subject Classifications:

• 62G05
• 62G07
• 62G08
• 62G20
• 62H12

Acknowledgements

Authors greatly thank the Editor in chief, the Associate Editor and the anonymous referees for a careful reading of the article and for their valuable comments and suggestions which improved the quality of this article substantially. They also extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under the project number R.G.P.2/68/41.