A Multi-Aspect Permutation Test for Goodness-of-Fit Problems

Abstract

Parametric techniques commonly rely on specific distributional assumptions. It is therefore fundamental to preliminarily identify the eventual violations of such assumptions. Therefore, appropriate testing procedures are required for this purpose to deal with a the goodness-of-fit (GoF) problem. This task can be quite challenging, especially with small sample sizes and multivariate data. Previous studiesshowed how a GoF problem can be easily represented through a traditional two-sample system of hypotheses. Following this idea, in this paper, we propose a multi-aspect permutation-based test to deal with the multivariate goodness-of-fit, taking advantage of the nonparametric combination (NPC) methodology. A simulation study is then conducted to evaluate the performance of our proposal and to identify the eventual critical scenarios. Finally, a real data application is considered.

Big Data Analytics and Machine Learning in Supply Chain 4.0: A Literature Review

“…The choice of test statistics is unrestricted and is simply driven by the nature of the data (e.g., binary, ordinal, or continuous) and of the comparison we want to conduct (e.g., if we are interested in comparing populations in terms of their cumulative distribution functions, mean values, or standard deviations). Different test statistics can be used at the same time too [83]. This makes NPC-based tests particularly flexible and suitable for a large variety of scenarios.…”