Abstract: We propose estimators for the counting process intensity function and its derivatives by maximizing the local partial likelihood. We prove the consistency and asymptotic normality of the proposed estimators. In addition to the computational ease, a nice feature of the proposed estimators is the automatic boundary bias correction property. We also discuss the choice of the tuning parameters in the definition of the estimators. An effective and easy-to-calculate data-driven bandwidth selector is proposed. A small simulation experiment is carried out to assess the performance of the proposed bandwidth selector and the estimators.
Key words and phrases: Asymptotic normality, automatic boundary correction, composite likelihood estimator, consistency, counting process, intensity function, local likelihood, local polynomial methods, martingale, maximum likelihood estimator, multiplicative intensity model, partial likelihood, point process, Z-estimator.