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.

中文翻译：

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通过剖面方法计算非参数凸危险估计量


本文提出了一种轮廓似然算法来计算凸风险函数的非参数最大似然估计。最大化分两个步骤执行：首先，使用支持减少算法来最大化具有给定最小值（或反模）点的所有危险函数的似然。然后表明，轮廓（或部分最大化）似然作为反模的函数是准凹的，因此可以应用二分算法来找到轮廓似然的最大值，从而也找到全局最大值。新算法使用人工和真实数据进行说明，包括加拿大男性和女性的一生数据。