Statistical inference for uniform stochastic ordering in several populations. (English) Zbl 0761.62038

Dykstra, Richard; Kochar, Subhash; Robertson, Tim

Ann. Stat. 19, No. 2, 870-888 (1991).

There are several stochastic orderings, such as the uniform stochastic ordering, the likelihood ratio ordering, the ordinary stochastic ordering and the failure rate ordering. The authors study statistical inference for uniform stochastic ordering in several populations. They consider mainly the following two problems: 1) The nonparametric maximum likelihood estimation in the generalized sense for \(k\)-population problems under uniform stochastic ordering restrictions; 2) the likelihood ratio statistic for testing equality of the \(k\) populations against the uniform stochastic ordering restriction. By a reparameterization the authors reduce the first problem to a well-known isotonic regression problem. They also derive the asymptotic distribution of the likelihood ratio statistic as the chi-bar-square type. An example for illustration of the theory is stated in the paper.

Reviewer: Fang Kai-tai (Hongkong)

MSC:

62G05	Nonparametric estimation
62E20	Asymptotic distribution theory in statistics

Keywords:

chi-bar-square distribution; empirical processes; likelihood ratio ordering; stochastic ordering; failure rate ordering; uniform stochastic ordering; nonparametric maximum likelihood estimation; \(k\)-population problems; likelihood ratio statistic; reparameterization; isotonic regression