Nonparametric Predictive Inference for Ordinal Data

Abstract

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this article, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, and briefly compared to NPI for non ordered categorical data. As application, the comparison of multiple groups of ordinal data is presented.

Keywords:

• Categorical data
• Lower and upper probabilities
• Multiple comparisons
• Nonparametric predictive inference
• Ordinal data

Mathematics Subject Classification:

• Primary 62G99
• Secondary 62A01, 62C099

Acknowledgments

P. Coolen-Schrijner, the second author, passed away in 2008. Before her death, she had initiated this research and achieved the first results reported in this article.