Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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A Note on the Chi-Square Test for Multivariate Normality Based on the Sample Mahalanobis Distances

  • Published : 1999.12.01
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Abstract

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

Keywords

References

  1. Information and Exponential Families in Statistical Theory Barndorff-Nielson, O.
  2. Normal Approximation and Asymptotic Expansions Bhattacharya, R.N.;Rao, R.R.
  3. The Annals of Probability v.6 Central Limit Theorems for Empirical Measures Dudley, R.M.
  4. The Annanls of Probability v.9 Some Conditional Limit Theorems in Exponential Families Holst, L.
  5. Distributions in Statistics: Continuous Multivariate Distributions Johnson, N.L.;Kotz, S.
  6. Applied Multivariate Statistical Analysis(Third Edition) Johnson, R.A.;Wichern, D.W.
  7. The Advanced Theory of Statistics: Volume 2 Inference and Relationship Kendall, S.M.;Stuart, A.S.
  8. Communications in Statistics - Theory and Methods v.10 Chi-square Tests for Multivariate Normality with Application to Common Stock Prices Moore, D.S.;Stubblebine, J.B.
  9. Communications in Statistics - Theory and Methods v.24 Some Remarks on the Chi-Squared Test with Both Margins Fixed Park, C.
  10. Z. Wahrsch. verw. Gebiete. v.50 General Chi-square Goodness-of-fit Tests with Data-dependent Cells Pollard, D.