A New Approach to the BHEP Tests for Multivariate Normality

Henze, Norbert; Wagner, Thorsten

doi:10.1006/jmva.1997.1684

Cited by 151 publications

(142 citation statements)

References 26 publications

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“…The local Gaussian model may not be valid for hyperspectral data if relatively small regions contain multiple materials. The BHEP (Barringhaus, Henze, Epps, and Pulley) test [23] was used to evaluate the local normal model. The BHEP test statistic compares the empirical characteristic function of the data, transformed to zero mean and identity covariance, with the characteristic function of the normal distribution having mean zero and identity covariance matrix.…”

Section: Local Normal Modelmentioning

confidence: 99%

Anomaly detection from hyperspectral imagery

Stein

Beaven

Hoff³

et al. 2002

IEEE Signal Process. Mag.

630

260

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H yperspectral sensors are a new class of optical sensor that collect a spectrum from each point in a scene. They differ from multispectral sensors in that the number of bands is much higher (20 or more) and the spectral bands are contiguous. For remote sensing applications, they are typically deployed on either aircraft or satellites. The data product from a hyperspectral sensor is a three-dimensional array or "cube" of data with the width and length of the array corresponding to spatial dimensions and the spectrum of each point as the third dimension. While this data cube is a convenient way to view the product, at most two of the dimensions can be acquired simultaneously. In the most common configuration, the spectral and one spatial dimension are acquired simultaneously to give a high quality spectral signature for each point in the scene. AVIRIS [1] and many other sensors directed toward terrain classification are flying spot sensors that acquire an image by raster scanning the scene in width while the platform moves to build up the second spatial dimension. More recently, the spatial resolution of hyperspectral sensors has been improved by using a two-dimensional focal plane array that simultaneously acquires a spectrum along a line of points in the scene. The second dimension is then built up by motion of the platform.

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Section: Local Normal Modelmentioning

confidence: 99%

Anomaly detection from hyperspectral imagery

Stein

Beaven

Hoff³

et al. 2002

IEEE Signal Process. Mag.

630

260

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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: 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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“…A careful analysis of the proof of Proposition 2.3 (to this end, observe that t 5 =0 if p=1Â2) shows that, for this symmetric normal mixture, we have n } b [14]), there is still a widespread belief that``directed'' tests like, e.g., those based on measures of skewness or kurtosis, should have specific diagnostic properties. That is, directed tests are presumed to be able to assess that a distribution is non-normal and at the same time to indicate the kind of departure from normality.…”

Section: To State the Limiting Behavior Of Bmentioning

confidence: 97%

Shortcomings of Generalized Affine Invariant Skewness Measures

Gutjahr

Henze

Folkers

1999

Journal of Multivariate Analysis

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This paper studies the asymptotic behavior of a generalization of Mardia's affine invariant measure of (sample) multivariate skewness. If the underlying distribution is elliptically symmetric, the limiting distribution is a finite sum of weighted independent / 2 -variates, and the weights are determined by three moments of the radial distribution of the corresponding spherically symmetric generator. If the population distribution has positive generalized skewness a normal limiting distribution occurs. The results clarify the shortcomings of generalized skewness measures when used as statistics for testing for multivariate normality. Loosely speaking, normality will be falsely accepted for a short-tailed non-normal elliptically symmetric distribution, and it will be correctly rejected for a long-tailed non-normal elliptically symmetric distribution. The wrong diagnosis in the latter case, however, would be rejection due to positive skewness. Academic PressAMS 1991 subject classifications: 62H10, 62H15, 60F05.

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A New Approach to the BHEP Tests for Multivariate Normality

Cited by 151 publications

References 26 publications

Anomaly detection from hyperspectral imagery

Anomaly detection from hyperspectral imagery

Comparison of some multivariate normality tests: A simulation study

Shortcomings of Generalized Affine Invariant Skewness Measures

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