Multivariate Kruskal –Wallis tests based on principal component score and latent source of independent component analysis

SummaryAnalysing multivariate and high-dimensional multi-sample data is essential in many scientific fields. One of the most crucial and popular topics in modern nonparametric statistics is multi-sample comparison problems for such multivariate and high-dimensional data. The Kruskal –Wallis test is widely used in the multi-sample problem. For multivariate or high-dimensional data, it is imperative to specify how to determine the ranks of individual vector-valued observations in terms of various distance metrics. Alternatively, one can combine the concept of principal componen t scores or independent component scores with the Kruskal–Wallis test. A simple but powerful Kruskal–Wallis test based on the principal component scores is discussed in this paper for the multivariate and high-dimensional data. Another type of Kruskal–Wallis test based on latent sources of ind ependent component analysis is constructed as a competitor. These tests are suitable for testing the difference in the location vector, scale matrix or both and can be used with equal and unequal sample sizes. These tests’ power performances are thoroughly compared with traditional distance-based Kruskal–Wallis tests for multivariate data using simulation based on Monte Carlo for various population distributions. We include an illustration of the proposed tests using real data. The paper concludes with some remarks and directions for future research.
Source: Australian and New Zealand Journal of Statistics - Category: Statistics Authors: Tags: Original Article Source Type: research