## Computation of nonparametric convex hazard estimators via profile methods.(English)Zbl 1161.62014

Summary: This paper proposes a profile likelihood algorithm to compute the nonparametric maximum likelihood estimator of a convex hazard function. The maximisation is performed in two steps: First the support reduction algorithm is used to maximise the likelihood over all hazard functions with a given point of minimum (or antimode). Then it is shown that the profile (or partially maximised) likelihood is quasi-concave as a function of the antimode, so that a bisection algorithm can be applied to find the maximum of the profile likelihood, and hence also the global maximum. The new algorithm is illustrated using both artificial and real data, including lifetime data for Canadian males and females.

### MSC:

 62G05 Nonparametric estimation 62N02 Estimation in survival analysis and censored data 65C60 Computational problems in statistics (MSC2010) 62A09 Graphical methods in statistics
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### References:

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