The generalized multisample Cucconi test statistic for the location and scale parameters

Nishino, Takuya; Murakami, Hidetoshi

doi:10.1080/00949655.2020.1774884

Cited by 2 publications

(1 citation statement)

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“…There are also several parametric and nonparametric tests for univariate multi_sample problems. See, for instance, B_ning (2000); B_ning & K_ssler (1997); Marozzi (2014); Murakami (2006, 2008); Nishino & Murakami (2018, 2020); Rubl_k (2005, 2007). However, when the data are multivariate, especially of higher dimension, in the sense that the number of variables is far too high compared to the available samples, there is still a shortage of efficient statistical tests for multi_sample comparisons.…”

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

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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.

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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

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A new distribution-free scheme for simultaneous Phase-I analysis of four process aspects and its application in monitoring customers’ waiting times

Suzuki¹,

Mukherjee²,

Murakami³

2023

Computers & Industrial Engineering

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The generalized multisample Cucconi test statistic for the location and scale parameters

Abstract: Mathematica code to obtain the exact moment of the MC K,p,q statistic.Listing 1: For the moment of C i, p,q .1 (* We obtain various moments by changing p and q) 2 3 p=2; 4 q=3; 5 s1[u_] := u^p; 6 s2[u_, n_] := (n + 1u)^q; 7 8 (About s1) 9 t1u[n1_, n_] := (n1/n)Sum[s1[u], {u, 1, n}];

Cited by 2 publications

References 28 publications

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

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

A new distribution-free scheme for simultaneous Phase-I analysis of four process aspects and its application in monitoring customers’ waiting times

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The generalized multisample Cucconi test statistic for the location and scale parameters

Abstract: Mathematica code to obtain the exact moment of the MC K,p,q statistic.Listing 1: For the moment of C i, p,q .1 (* We obtain various moments by changing p and q*) 2 3 p=2; 4 q=3; 5 s1[u_] := u^p; 6 s2[u_, n_] := (n + 1u)^q; 7 8 (*About s1*) 9 t1u[n1_, n_] := (n1/n)*Sum[s1[u], {u, 1, n}];

Cited by 2 publications

References 28 publications

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

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

A new distribution-free scheme for simultaneous Phase-I analysis of four process aspects and its application in monitoring customers’ waiting times

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Product

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About

Abstract: Mathematica code to obtain the exact moment of the MC K,p,q statistic.Listing 1: For the moment of C i, p,q .1 (* We obtain various moments by changing p and q) 2 3 p=2; 4 q=3; 5 s1[u_] := u^p; 6 s2[u_, n_] := (n + 1u)^q; 7 8 (About s1) 9 t1u[n1_, n_] := (n1/n)Sum[s1[u], {u, 1, n}];