Robustness of Nonparametric Predictive Inference for Future Order Statistics

Abstract

This paper considers robustness of Nonparametric Predictive Inference (NPI), in particular considering inference involving future order statistics. The concept of robust inference is usually aimed at development of inference methods which are not too sensitive to data contamination or to deviations from model assumptions. In this paper we use it in a slightly narrower sense. For our aims, robustness indicates insensitivity to small change in the data, as our predictive probabilities for order statistics and statistical inferences involving future observations depend upon the given observations. We introduce some concepts for assessing the robustness of statistical procedures to the NPI framework, namely sensitivity curve and breakdown point; these classical concepts require some adoption for application in NPI. Most of our nonparametric inferences have a reasonably good robustness with regard to small changes in the data.

Introducing Nonparametric Predictive Inference Methods for Reproducibility of Likelihood Ratio Tests

“…For these inferences NPI for Bernoulli quantities (Coolen, 1998) and for real-valued observations (Augustin and were used. Recently, presented NPI-RP for two basic nonparametric tests based on order statistics, namely a quantile test (Gibbons and Chakraborti, 2010) and a precedence test (Balakrishnan and Ng, 2006), using NPI for future order statistics (Alqifari, 2017;. These basic tests all enabled analytical results for NPI-RP.…”

Nonparametric predictive inference for comparison of two diagnostic tests

“…For this event NPI provides a precise probability, as each of the n+m n equally likely orderings of n past and m future observations has the r-th ordered future observation in precisely one interval I j . The event that the number of future observations in an interval (x a , x b ), denoted by C xa,x b , is greater than or equal to a particular value v, has the following precise probability (Alqifari, 2017),…”

Nonparametric predictive inference for diagnostic test thresholds

“…NPI for right-censored data was introduced by Coolen and Yan [19,20]. In Chapters 2 and 3, we apply NPI for future order statistics as presented by Coolen et al [16] and Alqifari [2], and in Chapter 4 we apply NPI for…”