Robust Differentiable Functionals for the Additive Hazards Model

Enrique E. Álvarez¹, Julieta Ferrario²

¹Schools of Economics and Engineering, Universidad Nacional de La Plata y CONICET, La Plata, Argentina.
²Department of Mathematics, Universidad Nacional de La Plata, Buenos Aires, Argentina.

DOI: 10.4236/ojs.2015.56064                

Abstract

In this article, we present a new family of estimators for the regression parameter β in the Additive Hazards Model which represents a gain in robustness not only against outliers but also against unspecific contamination schemes. They are consistent and asymptotically normal and furthermore, and they have a nonzero breakdown point. In Survival Analysis, the Additive Hazards Model proposes a hazard function of the form , where  is a common nonparametric baseline hazard function and z is a vector of independent variables. For this model, the seminal work of Lin and Ying (1994) develops an estimator for the regression parameter β which is asymptotically normal and highly efficient. However, a potential drawback of that classical estimator is that it is very sensitive to outliers. In an attempt to gain robustness, álvarez and Ferrarrio (2013) introduced a family of estimators for β which were still highly efficient and asymptotically normal, but they also had bounded influence functions. Those estimators, which are developed using classical Counting Processes methodology, still retain the drawback of having a zero breakdown point.

Keywords

Robust Estimation, Additive Hazards Model, Survival Analysis

Conflicts of Interest

The authors declare no conflicts of interest.

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