A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality

Romeu, Jorge Luis; Öztürk, A.

doi:10.1006/jmva.1993.1063

Cited by 99 publications

(58 citation statements)

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“…There is a continued interest in the problem of testing for multivariate normality, as evidenced by the recent papers of Ahn [1], Bowman and Foster [5], Henze [12], Horswell and Looney [14], Kariya and George [16], Koziol [17], Mudholkar, McDermott, and Srivastava [20], Mudholkar, Srivastava, and Lin [21], Naito [22], Ozturk and Romeu [23], Rayner, Best, and Matthews [24], Romeu and Ozturk [25], Singh [26], Versluis [27], and Zhu, Wong, and Fang [29] on this subject.…”

Section: Introductionmentioning

confidence: 95%

A New Approach to the BHEP Tests for Multivariate Normality

Henze

Wagner

1997

Journal of Multivariate Analysis

151

134

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Section: Introductionmentioning

confidence: 95%

A New Approach to the BHEP Tests for Multivariate Normality

Henze

Wagner

1997

Journal of Multivariate Analysis

151

134

View full text Add to dashboard Cite

“…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: 96%

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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“…The most powerful test of multivariate normality for a particular data set depends on the type of departure (e.g., both skewness and kurtosis, severe and moderately kurtic-prone alternatives) from multivariate normality exhibited by the data (Romeu and Ozturk 1993). However, the tests we used in this paper have been applied specifically for detecting discordancies and suspected causal variables, and the task-specific software (Scout) is readily available.…”

Section: Methodsmentioning

confidence: 98%

Application of two tests of multivariate discordancy to fisheries data sets

2007

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The generalized (Mahalanobis) distance and multivariate kurtosis are two powerful tests of multivariate discordancies (outliers). Unlike the generalized distance test, the multivariate kurtosis test has not been applied as a test of discordancy to fisheries data heretofore. We applied both tests, along with published algorithms for identifying suspected causal variable(s) of discordant observations, to two fisheries data sets from Lake Erie: total length, mass, and age from 1,234 burbot, Lota lota; and 22 combinations of unique subsets of 10 morphometrics taken from 119 yellow perch, Perca flavescens. For the burbot data set, the generalized distance test identified six discordant observations and the multivariate kurtosis test identified 24 discordant observations. In contrast with the multivariate tests, the univariate generalized distance test identified no discordancies when applied separately to each variable. Removing discordancies had a substantial effect on length-versus-mass regression equations. For 500-mm burbot, the percent difference in estimated mass after removing discordancies in our study was greater than the percent difference in masses estimated for burbot of the same length in lakes that differed substantially in productivity. The number of discordant yellow perch detected ranged from 0 to 2 with the multivariate generalized distance test and from 6 to 11 with the multivariate kurtosis test. With the kurtosis test, 108 yellow perch (90.7%) were identified as discordant in zero to two combinations, and five (4.2%) were identified as discordant in either all or 21 of the 22 combinations. The relationship among the variables included in each combination determined which variables were identified as causal. The generalized distance test identified between zero and six discordancies when applied separately to each variable. Removing the discordancies found in at least one-half of the combinations (k=5) had a marked effect on a principal components analysis. In particular, the percent of the total variation explained by second and third principal components, which explain shape, increased by 52 and 44% respectively when the discordancies were removed. Multivariate applications of the tests have numerous ecological advantages over univariate applications, including improved management of fish stocks and interpretation of multivariate morphometric data.

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A Comparative Study of Goodness-of-Fit Tests for Multivariate Normality

Cited by 99 publications

References 0 publications

A New Approach to the BHEP Tests for Multivariate Normality

A New Approach to the BHEP Tests for Multivariate Normality

Comparison of some multivariate normality tests: A simulation study

Application of two tests of multivariate discordancy to fisheries data sets

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