# Efficient Estimation Of Left-Truncated And Right Censored Data With Additive Hazard Model

## Authors

• Wissam Kamil Ghafil Kamil Ghafil Department of Mathematics, University of the-Qar, Iraq
• Riyadh R. Al-Mosawi Department of Mathematics, Thi-Qar University, Iraq.

## Abstract

In this paper, an additive hazard model is considered as a semiparametric model in which the unknown
parameter consists of finite dimensional and infinite dimensional parts with left truncated and right
censored data. The full likelihood function for the model is obtained for the parametric part and also for
the nonparametric part using linear sieve procedure and then compute the maximum likelihood estimators
for the two parts. The consistency of the maximum likelihood estimators is also proved for the two type
of parameters. The score operators for the parametric and nonparametric parts are obtained and their
adjoint score operators are computed. Finally, a simulation study using Monti-Carlo method and R
language is implemented to compute the maximum likelihood estimators and compare the results of the
proposed method with the true values. As a real life application, Stanford Heart transplant data is
considered and the maximum likelihood estimators are computed

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