Tests of multinormality based on location vectors and scatter matrices

Kankainen, Annaliisa; Taskinen, Sara; Oja, Hannu

doi:10.1007/s10260-007-0045-9

Cited by 43 publications

(33 citation statements)

References 26 publications

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“…Note that [9] used m 2 R − (p + 2)I p to test for (full) multivariate normality which is a special case here. Further note that the estimated projections (with respect to Mahalanobis inner product) to the noise and signal subspaces are given by…”

Section: Test Statistic For the Dimensionmentioning

confidence: 99%

Asymptotic and Bootstrap Tests for the Dimension of the Non-Gaussian Subspace

Nordhausen

Oja

Tyler

et al. 2017

IEEE Signal Process. Lett.

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Dimension reduction is often a preliminary step in the analysis of large data sets. The so-called non-Gaussian component analysis searches for a projection onto the non-Gaussian part of the data, and it is then important to know the correct dimension of the non-Gaussian signal subspace. In this paper we develop asymptotic as well as bootstrap tests for the dimension based on the popular fourth order blind identification (FOBI) method.Index Terms-Fourth order blind identification (FOBI), independent component analysis, non-Gaussian component analysis.

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Section: Test Statistic For the Dimensionmentioning

confidence: 99%

Asymptotic and Bootstrap Tests for the Dimension of the Non-Gaussian Subspace

Nordhausen

Oja

Tyler

et al. 2017

IEEE Signal Process. Lett.

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“…The sample statistics can then be used to test multivariate normality, for example. For their limiting distributions under the normality assumption, see, for example, Kankainen, Taskinen and Oja (2007). For other extensions of multivariate skewness and kurtosis and their connections to skewness and kurtosis measures above, see Kollo (2008) and Kollo and Srivastava (2004).…”

Section: Measures Of Multivariate Skewness and Kurtosismentioning

confidence: 99%

Fourth Moments and Independent Component Analysis

Miettinen¹,

Taskinen²,

Nordhausen³

et al. 2015

Statist. Sci.

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Abstract. In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting with the corresponding optimization problems, deriving the estimating equations and estimation algorithms, and finding asymptotic statistical properties of the estimates. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases JADE and the symmetric version of FastICA perform better than their competitors.

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“…The test based on * rejects H0 at a test size α if W * < c α; n, p , where c α; n, p satisfies the equation = Ρ{ * < ; , | 0 holds}. Kankainen et al (2007) obtained generalizations of classical Mardia's measures of skewness and kurtosis by using special choices of location and scatter estimators.…”

Section: Villasenor-alva and Gonzalez-estrada's Generalized Shapiro-wmentioning

confidence: 99%

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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Tests of multinormality based on location vectors and scatter matrices

Abstract: Affine invariance, Kurtosis, Pitman efficiency, Skewness,

Cited by 43 publications

References 26 publications

Asymptotic and Bootstrap Tests for the Dimension of the Non-Gaussian Subspace

Asymptotic and Bootstrap Tests for the Dimension of the Non-Gaussian Subspace

Fourth Moments and Independent Component Analysis

Comparison of some multivariate normality tests: A simulation study

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