Two new distribution-free two-sample tests for versatile alternative

Mukherjee, Amitava; Kössler, Wolfgang; Murakami, Hidetoshi

doi:10.1080/02331888.2021.1998053

Cited by 5 publications

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, it would also be interesting to look into the scale aspect. For the location_scale test, see, for example, B_ning (2002); B_ning & Thadewald (2000); K_ssler (1999); K_ssler & Mukherjee (2020); Marozzi (2009, 2013); Mukherjee, K_ssler & Murakami (2021); Murakami (2006, 2007, 2012); Neuh_user (2000, 2001); Neuh_user, Welz & Ruxton (2017). There are also several parametric and nonparametric tests for univariate multi_sample problems.…”

Section: Introductionmentioning

confidence: 99%

Multivariate Kruskal_Wallis tests based on principal component score and latent source of independent component analysis

Mukherjee

Murakami

2022

Aus NZ J of Statistics

Self Cite

View full text Add to dashboard Cite

Summary Analysing 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 component 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 independent 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Multivariate Kruskal_Wallis tests based on principal component score and latent source of independent component analysis

Mukherjee

Murakami

2022

Aus NZ J of Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

Nonparametric tests for combined location-scale and Lehmann alternatives using adaptive approach and max-type metric

Funato,

Murakami,

Kössler

et al. 2024

J. Korean Stat. Soc.

View full text Add to dashboard Cite

The paper deals with the classical two-sample problem for the combined location-scale and Lehmann alternatives, known as the versatile alternative. Recently, a combination of the square of the standardized Wilcoxon, the standardized Ansari–Bradley and the standardized Anti-Savage statistics based on the Euclidean distance has been proposed. The Anti-Savage test is the locally most powerful rank test for the right-skewed Gumbel distribution. Furthermore, the Savage test is the locally most powerful linear rank test for the left-skewed Gumbel distribution. Then, a test statistic combining the Wilcoxon, the Ansari–Bradley, and Savage statistics is proposed. The limiting distribution of the proposed statistic is derived under the null and the alternative hypotheses. In addition, the asymptotic power of the suggested statistic is investigated. Moreover, an adaptive test is proposed based on a selection rule. We compare the power performance against various fixed alternatives using Monte Carlo. The proposed test statistic displays outstanding performance in certain situations. An illustration of the proposed test statistic is presented to explain a biomedical experiment. Finally, we offer some concluding remarks.

show abstract