Journal ArticleDOI
A class of invariant consistent tests for multivariate normality
Norbert Henze,B. Zirkler +1 more
Reads0
Chats0
TLDR
In this article, the authors present a class of afflne-invariant tests for the composite hypothesis H d the law of X 1 is a non-degenerate normal distribution which are consistent against any fixed non-normal alternative distribution.Abstract:
Let be independent identically distributed random vectors in Rd d ≥ 1 , with sample mean [Xbar] n and sample covariance matrix S n . We present a class of practicable afflne-invariant tests for the composite hypothesis H d the law of X 1 is a non-degenerate normal distribution which are consistent against any fixed non- normal alternative distribution. The test statistic is a weighted integral of the squared modulus of the difference between the empirical characteristic function of the scaled residuals and its pointwise limit under H d - An alternative representation is given in terms of an L 2-distance between densities. The limiting null distribution of the test statistic is obtained. Power performance of the new tests is assessed in a Monte Carlo study.read more
Citations
More filters
Journal ArticleDOI
MVN: An R Package for Assessing Multivariate Normality
TL;DR: An R package, MVN, which contains the three most widely used multivariate normality tests, including Mardia's, Henze-Zirkler's and Royston's, and graphical approaches, including chi-square Q-Q, perspective and contour plots, and includes two multivariate outlier detection methods, which are based on robust Mahalanobis distances.
Journal ArticleDOI
Energy statistics: A class of statistics based on distances
TL;DR: Energy distance is a statistical distance between the distributions of random vectors, which characterizes equality of distributions as mentioned in this paper, and there is an elegant relation to the notion of potential energy between statistical observations.
Book
Theory of multivariate statistics
Martin Bilodeau,David Brenner +1 more
TL;DR: Linear algebra as discussed by the authors, Gamma, Dirichlet, and F distributions, and Wishart distributions are used for linear algebra and linear algebra is used for robustness and robustness.
Journal ArticleDOI
A new test for multivariate normality
Gábor J. Székely,Maria L. Rizzo +1 more
TL;DR: In this paper, a new class of rotation invariant and consistent goodness-of-fit tests for multivariate distributions based on Euclidean distance between sample elements is proposed, which applies to any multivariate distribution with finite second moments.
Journal ArticleDOI
Contribution to Productivity or Pork Barrel? : The Two Faces of Infrastructure Investment
TL;DR: In this paper, a simultaneous-equation approach to the estimation of the contribution of transport infrastructure accumulation to regional growth is proposed, and empirical findings on a panel of France's regions over 1985-92 suggest that electoral concerns and influence activities were significant determinants of the cross-regional allocation of transportation infrastructure investments.
References
More filters
Journal ArticleDOI
An Analysis of Variance Test for Normality (Complete Samples)
S. S. Shapiro,M. B. Wilk +1 more
TL;DR: In this article, a new statistical procedure for testing a complete sample for normality is introduced, which is obtained by dividing the square of an appropriate linear combination of the sample order statistics by the usual symmetric estimate of variance.
BookDOI
Density estimation for statistics and data analysis
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Journal ArticleDOI
Measures of multivariate skewness and kurtosis with applications
TL;DR: In this article, the authors developed measures of multivariate skewness and kurtosis by extending certain studies on robustness of the t statistic, and the asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test for multivariate normality is proposed.
Book
Empirical processes with applications to statistics
Galen R. Shorack,Jon A. Wellner +1 more
TL;DR: In this paper, a broad cross-section of the literature available on one-dimensional empirical processes is summarized, with emphasis on real random variable processes as well as a wide-ranging selection of applications in statistics.
Book
Symmetric Multivariate and Related Distributions
TL;DR: In this article, the authors define marginal distributions, moments and density marginal distributions moments density the relationship between (phi and f) conditional distributions properties of elliptically symmetric distributions mixtures of normal distributions robust statistics and regression model robust statistics regression model log-elliptical and additive logistic elliptical distributions multivariate log elliptical distribution additive logistics elliptical distribution complex elliptical symmetric distribution.