Nonparametric Predictive Inference for Multiple Future Ordinal Observations

Abstract

Nonparametric predictive inference (NPI) is a statistical methodology based on the assumption A_(n) proposed by Hill for the prediction of a future observation. NPI uses lower and upper probabilities to quantify uncertainty. NPI has been developed for various data types, and the explicitly predictive nature of NPI makes the method particularly attractive and well-suited for a wide variety of statistical applications. This thesis proposes novel contributions to statistical methods for ordinal data using the NPI method with multiple future observations. The method uses a latent variable representation of the data observations and ordered categories on the real-line.

NPI lower and upper probabilities for several events involving multiple future ordinal observations are presented. The NPI method is applied to selection problems involving multiple future ordinal observations. Pairwise comparison of future observations from two independent groups is presented. The accuracy of diagnostic tests with ordinal outcomes is considered, with NPI-based methods introduced for selecting the optimal thresholds of a diagnostic test, initially for two-group classification and then extended to three-group classification.

To illustrate the proposed NPI methods, examples using data from the literature are provided. Simulation studies are conducted to investigate the predictive performance of the proposed methods for selecting diagnostic test thresholds and to compare these methods with classical methods, such as the Youden index, Liu index and maximum volume methods. The results indicate that the NPI methods tend to outperform the classical approaches by correctly classifying more individuals in each group. Overall, the number of future observations considered influences the NPI lower and upper probabilities, affecting category selection, pairwise comparison, and diagnostic threshold selection.