Non-parametric predictive inference for future order statistics

ABSTRACT

This article presents non-parametric predictive inference for future order statistics. Given the data consisting of n real-valued observations, m future observations are considered and predictive probabilities are presented for the rth-ordered future observation. In addition, joint and conditional probabilities for events involving multiple future order statistics are presented. The article further presents the use of such predictive probabilities for order statistics in statistical inference, in particular considering pairwise and multiple comparisons based on two or more independent groups of data.

KEYWORDS:

• Future order statistics
• Lower and upper probabilities
• Multiple comparisons
• Non-parametric predictive inference
• Pairwise comparisons.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62A99
• 62G30
• 62J15

Acknowledgments

The authors are grateful to two anonymous reviewers whose supportive comments led to improved presentation of the article. The authors dedicate this article to Professor Paul van der Laan (Eindhoven University of Technology, The Netherlands), who passed away in July 2016. Paul was PhD supervisor of the first-named author and “scientific grandfather” of the other two authors. He published on a variety of topics in statistics, including selection methods and non-parametrics. He was an excellent statistician, motivating teacher and supervisor, and a kind and supportive person who is much missed.