A new test for multivariate normality

By G'abor J. Sz'ekely, Maria L. Rizzo. 2005

373 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, neutral): “The energy distance between probability distributions P and Q as proposed in Székely and Rizzo (2004; 2005) is given by DE(P,Q) = 2EXY ‖X − Y ‖ − EXX′‖X −X ′‖ − EY Y ′‖Y − Y ′‖, (5.2) where X,X ′ ∼ P and Y, Y ′ ∼ Q.”
A Kernel Test of Goodness of Fit (2016, methodology): “A different smoothing scheme in the frequency domain results in an energy distance statistic (this likewise being an MMD with a particular choice of kernel; see Sejdinovic et al., 2013), which can be used in a test of normality (Székely & Rizzo, 2005).”
Equivalence of distance-based and RKHS-based statistics in hypothesis testing (2012, neutral): “Let k be a measurable kernel on Z , and denote, for θ > 0, , by the Riesz representation theorem.”
Hypothesis testing using pairwise distances and associated kernels (2012, methodology): “…a dramatic improvement for the sinusoidal perturbation, compared with the case q = 1 and the Gaussian kernel: values q = 1/3 (and smaller) yield virtually error-free performance even at high frequencies (note that q = 1 corresponds to the energy distance described in Székely & Rizzo (2004; 2005)).”
Distance covariance in metric spaces (2011, background): “[These notions were conflated in SRB and Székely and Rizzo (2005a, 2005b).]”
Nonparametric Tests for Serial Independence Based on Quadratic Forms (2005, neutral): “In contrast to some other tests based on quadratric functionals, such as that of Székely and Rizzo (2005), there is no need to impose any conditions on the moments of the time series.”
An empirical goodness-of-fit test for multivariate distributions (2013, methodology): “Székely and Rizzo [27] proposed a test that is applicable to any multivariate distribution having finite second moments, but the test is applied only to the multivariate normal, as analytical derivation of the test statistic in other settings is likewise unmanageable.”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “We define the measure of Gaussianization of the residuals as G = Energy(zx→y)− Energy(zy→x), where Energy(·) computes the statistic of the energy distance test for Gaussianity described in (Székely and Rizzo, 2005).”
Detecting relevant changes in time series models (2014, background): “6), such that F1 and F2 have moments of order one [see Székely and Rizzo (2005), p.”
Energy statistics: A class of statistics based on distances (2013, methodology): “(vi) Change point analysis based on Székely and Rizzo (2004) is applied in Kim et al. (2009) and Matteson and James (2012).”