The ordering of future observations from multiple groups

TL;DR

This paper introduces a nonparametric predictive inference method to assess the probability that future observations from multiple groups will follow a specific order, aiding in comparisons and decision-making.

Contribution

It develops a novel NPI approach for predicting and quantifying uncertainty in the ordering of future observations across multiple independent groups.

Findings

NPI provides valid probability bounds for ordered future observations.

Applications include group comparison, diagnostic accuracy, and ranked set sampling.

Method offers a flexible, assumption-free framework for multi-group inference.

Abstract

There are many situations where comparison of different groups is of great interest. Considering the ordering of the efficiency of some treatments is an example. We present nonparametric predictive inference (NPI) for the ordering of real-valued future observations from multiple independent groups. The uncertainty is quantified using NPI lower and upper probabilities for the event that the next future observations from these groups are ordered in a specific way. Several applications of these NPI lower and upper probabilities are explored, including multiple groups inference, diagnostic accuracy and ranked set sampling.