Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from https://doi.org/10.1007/BF02613322 below:

A consistent test for multivariate normality based on the empirical characteristic function

LetX ₁,X ₂, …,X _n be independent identically distributed random vectors in IR^d,d ⩾ 1, with sample mean\(\bar X_n \) and sample covariance matrixS _n. We present a practicable and consistent test for the composite hypothesisH _d: the law ofX ₁ is a non-degenerate normal distribution, based on a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residualsS ^−1/2 _n (X _j −\(\bar X_n \)) and its pointwise limit exp (−1/2|t|²) underH _d. The limiting null distribution of the test statistic is obtained, and a table with critical values for various choices ofn andd based on extensive simulations is supplied.

This is a preview of subscription content, log in via an institution to check access.

Springer+

from €39.99 /Month

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

• Baringhaus L, Danschke R, Henze N (1988) Recent and classical tests for normality — a comparative study. Comm Statist B Comp Simul (submitted)

• Cox DR, Small NJH (1978) Testing multivariate normality. Biometrika 65:263–272

  Article  MATH  Google Scholar 

• Csörgő S (1986) Testing for normality in arbitrary dimension. Ann Statist 14:708–723

  MathSciNet  Google Scholar 

• De Wet T, Randles RH (1987) On the effect of substituting parameter estimators in limitingx ²,U andV statistics. Ann Statist 15:398–412

  MATH  MathSciNet  Google Scholar 

• Eaton MR, Perlman MD (1973) The non-singularity of generalized sample covariance matrices. Ann Statist 1:710–717

  MATH  MathSciNet  Google Scholar 

• Epps TW, Pulley LB (1983) A test for normality based on the empirical characteristic function. Biometrika 70:723–726

  Article  MATH  MathSciNet  Google Scholar 

• Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugenics 7/II:179–188

  Google Scholar 

• Gnanadesikan R (1977) Methods for statistical data analysis of multivariate observations. Wiley, New York.

  MATH  Google Scholar 

• Koziol JA (1982) A class of invariant procedures for assessing multivariate normality. Biometrika 69:423–427

  Article  MATH  MathSciNet  Google Scholar 

• Koziol JA (1983) On assessing multivariate normality. J Roy Statist Soc Ser B 45:358–361

  MATH  MathSciNet  Google Scholar 

• Mardia KV (1980) Tests of univariate and multivariate normality. In: Krishnaiah PR (ed) Handbook of statistics, I Analysis of variance. North-Holland, Amsterdam, pp 279–320

  Google Scholar 

Download references

1. Institut für Mathematische Stochastik, Universität Hannover, Welfengarten 1, D-3000, Hannover 1, FRG

   L. Baringhaus &  N. Henze

1. L. Baringhaus
2. N. Henze

Baringhaus, L., Henze, N. A consistent test for multivariate normality based on the empirical characteristic function. Metrika 35, 339–348 (1988). https://doi.org/10.1007/BF02613322

Download citation

• Received: 26 December 1988

• Issue Date: December 1988

• DOI: https://doi.org/10.1007/BF02613322

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4