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

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

Let S 1 , S 2 , ? , S k be survival functions of life distributions. They are said to be uniformly stochastically ordered, S 1 ? u s o S 2 ? u s o ? ? u s o S k , if S i / S i + 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.

Hammou El Barmi | Hari Mukerjee | H. Mukerjee | H. Barmi

[1] F. T. Wright. Order-Restricted Inferences , 2006 .

[2] H. D. Brunk,et al. Statistical inference under order restrictions : the theory and application of isotonic regression , 1973 .

[3] J. M. Bremner,et al. Statistical Inference under Restrictions , 1973 .

[4] J. Rojo,et al. On Estimating a Survival Curve Subject to a Uniform Stochastic Ordering Constraint , 1993 .

[5] H. Mukerjee. Estimation of Survival Functions under Uniform Stochastic Ordering , 1996 .

[6] On nonparametric maximum likelihood estimation of a distribution uniformly stochastically smaller than a standard , 1991 .

[7] Laurence L. George,et al. The Statistical Analysis of Failure Time Data , 2003, Technometrics.

[8] On the asymptotic distribution theory of a class of consistent estimators of a distribution satisfying a uniform stochastic ordering constraint , 2000 .

[9] Stochastic Orders , 2008 .

[10] Yazhen Wang. A Likelihood Ratio Test against Stochastic Ordering in Several Populations , 1996 .

[11] J. Kalbfleisch,et al. The Statistical Analysis of Failure Time Data , 1980 .

[12] R. Dykstra,et al. Statistical inference for uniform stochastic ordering in several populations , 1991 .