Consistent estimation of survival functions under uniform stochastic ordering; the k-sample case

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Authors
El Barmi, Hammou
Mukerjee, Hari
Issue Date
2016-02
Type
Article
Language
en_US
Keywords
Consistency , Estimation , Isotonic regression , Uniform stochastic ordering
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Abstract

Let S-1, S-2, ... , S-k be survival functions of life distributions. They are said to be uniformly stochastically ordered, S-1 <=(uso) S-2 <=(uso) ... <=(uso) S-k, if S-i/Si+1 is a survival function for 1 <= i <= k - 1. The nonparametric maximum likelihood estimators of the survival functions subject to this ordering constraint are known to be inconsistent in general. Consistent estimators were developed only for the case of k = 2. In this paper we provide consistent estimators in the k-sample case, with and without censoring. In proving consistency, we needed to develop a new algorithm for isotonic regression that may be of independent interest.

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El Barmi, Hammou; Mukerjee, Hari. 2016. Consistent estimation of survival functions under uniform stochastic ordering; the k-sample case. Journal of Multivariate Analysis, vol. 144, February 2016:pp 99–109
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Elsevier B.V.
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0047-259X
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