Inferences on Several Survival Functions Under Uniform Stochastic Ordering

• Activity Number: 627
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hammou El Barmi*+ and Hari Mukerjee
• Companies: Baruch College and Wichita State University
• Keywords: Uniform stochastic ordering ; isotonic regression ; consistency ; hypothesis testing

Abstract

Let $T_1,T_2,\ldots,T_k$ be survival functions of life distributions. They are said to be uniformly stochastically ordered, $T_1\uso T_2\uso\cdots\uso T_k$, if $T_i/T_{i+1}$ is a survival function for $1\le i\le k-1.$ The nonparametric maximum likelihood estimators of the survival functions subject to the ordering constraint, based on independent random samples, are known to be inconsistent in general for cases other than the multinomials with a common support. Consistent estimators were developed in the case of $k=2$ in the early 1990's; however, the general $k$-sample case had been elusive. In this talk we provide uniformly strongly consistent estimators in the $k$-sample case with no restrictions on the survival functions. These estimators are applicable to both the uncensored and censored cases. We also develop a test of homogeneity against uniform stochastic ordering a real life data is analyzed in order to illustrate the theoretical results.