The Linear Stochastic Order and Directed Inference for Multivariate Ordered Distributions with Applications

• Activity Number: 320
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Ori Davidov*+ and Shyamal Peddada
• Companies: University of Haifa and National Institute of Environmental Health Sciences
• Keywords: dose-response studies ; nonparametric tests ; order restricted statistical inference ; nonparametric teststochastic order relations

Abstract

Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two sided alternatives they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy's classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a a 90--day pre--chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP). Not only is the proposed methodology more sensitive in detecting a dose-related increase in response, but is also simple to use.