Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Simple Chi-squared Test of Multivariate Normality Based on the Spherical Data

  • Published : 2001.04.01
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Abstract

We provide a simple chi-squared test of multivariate normality based on rectangular cells on the spherical data. This test is simple since it is a direct extension of the univariate chi-squared test to multivariate case and the expected cell counts are easily computed. We derive the limiting distribution of the chi-squared statistic via the conditional limit theorems. We study the accuracy in finite samples of the limiting distribution and then compare the poser of our test with those of other popular tests in an application to a real data.

Keywords

References

  1. Annals of Mathematical Statistics v.25 The Use of Maximum Likelihood Estimates in x² Tests for Goodness of Fit Chernoff,H.;Lehmann,E.L.
  2. Annals of Probability v.9 Some Conditional Limit Theorems in Exponential Families Holst,L.
  3. Biometrika v.57 Measures of Multivariate Skewness and Kurtosis with Applications Mardia,K.V.
  4. Annals of Statistics v.3 Unified Large-sample Theory of General Chi-squared Statistics for Tests of Fit Moore,D.S.;Spruill,M.C.
  5. Theory of Probability and Its Applications v.18 Chi-Square Test for Continuous Distributions with Shift and Scale Parameters Nikulin,M.S.
  6. Communications in Statistics-Simulations and Computation v.21 A New Method for Assessing Multivariate Normality with Graphical Applications Ozturk,A.;Romeu,J.L.
  7. Communications in Statistics - Theory and Methods v.24 Some Remarks on the Chi-squared Test with Both Margins Fixed Park,C.
  8. The Korean Communications in Statistics v.5 On the Distributions of the Scaled Residuals under Multivariate Normal Distributions Park.C.
  9. Journal of the Korean Statistical Society v.28 A Note on the Chi-Square Test for Multivariate Normality Based on the Sample Mahalanobis Distances Park.C.
  10. Z. Wahrsch. verw. Gebiete v.50 General Chi-square Goodness-of-fit Tests with Data Dependent Cells Pollard,D.
  11. Communications in Statistics v.3 A Chi-Square Statistic for Goodness-of-Fit Tests within the Exponential Family Rao,C.R.;Robson,D.S.
  12. Journal of Multivariate Analysis v.46 A Comparative Study of Goodness-of-fit Tests for Multivariate Normality Romeu,J.L.;Ozturk,A.
  13. Biometrika v.52 An Analysis of Variance Test for Normality(Complete Samples) Shapiro,S.S.;Wilk,M.B.
  14. Biometrika v.44 The x² Goodness-of-fit Test for Normal Distributions Watson,G.S.