On estimation of the hazard function for doubly truncated data

Elbay, Roumaissa (2025) On estimation of the hazard function for doubly truncated data. Doctoral thesis, Université Mohamed Khider (Biskra - Algérie).

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Abstract

In this thesis, we investigate the problem of incomplete data, specifically the phenomenon of double truncation, which make working with classical methods very hard, as truncation mean the loss of samples during the statistical analysis, and leads to negative results of the study and wrong decisions. Specifically, we focused in this thesis on estimating of the hazard function in the case of double truncation, where estimating the hazard function estimator is defined in many previous work, hence we make comparison with the hazard functions known in this case and our proposed estimator, and thus we result that the proposed hazard function estimator is more accurate through applied and theoretical comparison. In addition, a smoother cumulative distribution function estimator was proposed, as the previously proposed estimator of the distribution function it was not smooth and not continuous. In this context, several methods were also proposed to obtain the smoothing parameter for the cumulative distribution function within the data subject to double truncation.

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