New nonparametric tests for testing homogeneity of scale parameters against umbrella alternative

2012 ◽  
Vol 82 (9) ◽  
pp. 1681-1689 ◽  
Author(s):  
Anil Gaur ◽  
Kalpana K. Mahajan ◽  
Sangeeta Arora
Keyword(s):  
Nonparametric Tests ◽  
Scale Parameters ◽  
Umbrella Alternative ◽  
Testing Homogeneity

scholarly journals Nonparametric Tests for the Umbrella Alternative with Unknown Peak in a Mixed Design

2020 ◽  
pp. 1-13
Author(s):  
Hassan Alsuhabi ◽  
Rhonda Magel
Keyword(s):  
Simulation Study ◽  
Nonparametric Tests ◽  
Asymptotic Distributions ◽  
Test Statistics ◽  
Mixed Design ◽  
Randomized Design ◽  
Umbrella Alternative ◽  
Unknown Peak ◽  
Completely Randomized Design ◽  
Better Than

Aims: Introducing and comparing 4 different tests for the unknown umbrella alternative in a mixed design. Study Design: Simulation study consisting of a randomized complete block portion and a completely randomized design portion for various underlying distributions. Place and Duration of Study: Simulation Study – conducted at North Dakota State University from September 2018 through December 2019. Methodology: This paper proposes four non-parametric tests for testing the umbrella alternative with unknown peak when the data are mixture of a randomized complete block and a completely randomized design. The proposed tests are various combinations of a modified (unmodified) Mack-Wolfe’s test and a modified (unmodified) Kim-Kim’s test, respectively. In this paper, the proposed tests are an extension of Magel et al. (2010) and Hassan and Magel (2020) peak known tests to the unknown peak setting. The four proposed test statistics are compared to each other. Results: When there were 3 populations, the unmodified versions of the test statistics did better than the modified versions.  When there were 4 and 5 populations, the results varied. Conclusion: All of the test statistics reached their asymptotic distributions quickly.  The standardize first versions of the test statistics were generally better than the standardized last version of the test statistics, which meant that it was better to place equal weights on the RCBD portion and the CRD portion.

scholarly journals Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions

2019 ◽  
Vol 42 (2) ◽  
pp. 185-208
Author(s):  
Atul Rajaram Chavan ◽  
Digambar Tukaram Shirke
Keyword(s):  
Real Life ◽  
Nonparametric Tests ◽  
Data Depth ◽  
Multivariate Distributions ◽  
Data Set ◽  
Scale Parameters ◽  
Real Life Data ◽  
Nonparametric Combination ◽  
Combination Theory ◽  
Illustrative Purpose

In this article, we propose nonparametric tests for simultaneously testing equality of location and scale parameters of two multivariate distributions by using nonparametric combination theory. Our approach is to combine the data depth based location and scale tests using combining function to construct a new data depth based test for testing both location and scale parameters. Based on this approach, we have proposed several tests. Fisher's permutation principle is used to obtain p-values of the proposed tests. Performance of proposed tests has been evaluated in terms of empirical power for symmetric and skewed multivariate distributions and compared to the existing test based on data depth. The proposed tests are also applied to a real-life data set for illustrative purpose.

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