New tests for multivariate normality based on Small's and Srivastava's graphical methods

Hanusz, Zofia; Tarasinska, J

doi:10.1080/00949655.2011.594051

Cited by 11 publications

(6 citation statements)

References 13 publications

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“…Some recent references are Thulin (2014), Hanusz and Tarasińska (2012), Delmail et al (2011), Tenreiro (2011), Cardoso De Oliveira andFerreira (2010), Okamoto and Seo (2010), Villasenor Alva and Estrada (2009). It can also be seen reviews by Liang et al (2009), Koizumi et al (2009), Hanusz and Tarasińska (2008), Doornik and Hansen (2008), Farrell et al (2007), Arcones (2007), Sürücü (2006), Holgersson (2006), Székely and Rizzo (2005), Pudelko (2005), Mecklin and Mundfrom (2005), Dufour et al (2003), Burdenski (2000), Henze and Wagner (1997), Henze (1997), Looney (1995), Romeu and Ozturk (1993), and Henze and Zirkler (1990).…”

Section: Introductionmentioning

confidence: 92%

Comparison of some multivariate normality tests: A simulation study

Alpu¹,

Yuksek

2016

Int. j. adv. appl. sci

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Many classical multivariate statistical methods are mostly based on the assumption of multivariate normality. Departures from normality, called non-normality, render those statistical methods inaccurate, so it is important to know if datasets are normal or non-normal. Especially in medical and life sciences, most statistical tests required the assumption of multivariate normality have been extensively used. In this study, after summarizing the properties of several most widely used multivariate normality tests, we aim to compare the power and type I error rates of these tests, which have been developed in recent years by many researchers. So, the reader will elucidate the differences and the similarities/superiorities and weaknesses of the tests in order to make the appropriate choice in their practical applications. For this purpose we carried a Monte Carlo simulation study with nominal α level, small, medium and large sample size, different dimension and multivariate distributions which includes different skewness and kurtosis. In conclusion, the results obtained from the comparative study are given.

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Section: Introductionmentioning

confidence: 92%

Comparison of some multivariate normality tests: A simulation study

Alpu¹,

Yuksek

2016

Int. j. adv. appl. sci

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“…when n ≤ p , the estimated covariance matrix is non-invertible. The projection methods of [41] and the method based on Srivastava’s graphical method in [42] are applicable in this HDLSS setting, but no open implementations of the methods exist for power evaluation. The methods of Liang in [43, 44] are also applicable in the HDLSS setting and open implementations exist.…”

Section: Resultsmentioning

confidence: 99%

A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario

2019

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Two classical multivariate statistical problems, testing of multivariate normality and the k-sample problem, are explored by a novel analysis on several resolutions simultaneously. The presented methods do not invert any estimated covariance matrix. Thereby, the methods work in the High Dimension Low Sample Size situation, i.e. when n ≤ p. The output, a significance map, is produced by doing a one-dimensional test for all possible resolution/position pairs. The significance map shows for which resolution/position pairs the null hypothesis is rejected. For the testing of multinormality, the Anderson-Darling test is utilized to detect potential departures from multinormality at different combinations of resolutions and positions. In the k-sample case, it is tested whether k data sets can be said to originate from the same unspecified discrete or continuous multivariate distribution. This is done by testing the k vectors corresponding to the same resolution/position pair of the k different data sets through the k-sample Anderson-Darling test. Successful demonstrations of the new methodology on artificial and real data sets are presented, and a feature selection scheme is demonstrated.

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“…The first step in this analysis is to check whether or not the data set meets the normality assumption by using the Shapiro-Wilk test and homogeneity variances by Levene's test. Shapiro-Wilk test is generally more powerful than the Kolmogorov-Smirnov test [34,35]. Shapiro-Wilk test can be used when the sample size is between 3 and 5,000 [36].…”

Section: Comparison Analysis Of Duration and Distance Between Recurring Earthquake Eventsmentioning

confidence: 99%

Earthquake behavior in Sumatra territory based on time and distance between consecutive large event

Anwar

2022

E3S Web Conf.

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The purpose of this study is to understand the behavior of earthquakes with a specific magnitude (M) in the Sumatra territory based on their duration of time and the distance between two earthquakes that happen consecutively. We explore 1,641 data sets of duration and distances with a specific magnitude that were generated from 458 earthquakes with M ≥ 5.0 during 2009-2017. This study revealed that the occurrence of the later (second) earthquake at any location (referred to in this paper as a recurring earthquake) with a bigger or equal magnitude as the previous one depends on duration especially for magnitude under 5.8. The comparison analyses showed that the recurring earthquake events tended to have similar average distances. However, the length of time between two earthquakes is different for lower magnitudes (under 6.0), whereas between an earthquake and a recurring earthquake with a magnitude above 6.0, the length of time tends to be similar.

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New tests for multivariate normality based on Small's and Srivastava's graphical methods

Cited by 11 publications

References 13 publications

Comparison of some multivariate normality tests: A simulation study

Comparison of some multivariate normality tests: A simulation study

A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario

Earthquake behavior in Sumatra territory based on time and distance between consecutive large event

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