Stochastic Ordering Regression: A Semiparametric Approach to Modeling the Stochastic Ordering of Response Variables Conditional on Predictors

• Activity Number: 112
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Olivier Thas*+ and Jan R. De Neve and Lieven Clement and Jean-Pierre Ottoy
• Companies: Ghent University and Ghent University and Ghent University and Ghent University
• Keywords: semiparametric inference ; stochastic ordering ; rank statistics ; regression models

Abstract

Statisticians are often interested in modeling the conditional distribution of a response variable, say $Y$, given a vector of predictors, say $x$. Let $Y(x)$ denote a random variable with this conditional distribution. Traditional linear regression can then be represented as $E(Y(x))=x^t \beta$. Instead of focusing on the conditional mean, however, we present a semiparametric framework that allows statistical inference on the conditional stochastic ordering of the response variable. In particular, we model the probabilities $P(Y(x)\leq Y(x))$ in terms of the predictors $x$ and $z$. In simple settings the methods reduce to Mann-Whitney and Kruskal-Wallis statistics. Our stochastic ordering regression is thus a generalization of those rank methods. In this paper we present the basic semiparametric theory and illustrate the rich interpretability by examples.