On testing homogeneity of variances for nonnormal models using entropy

• Bartlett MS (1937) Properties of sufficiency and statistical tests. Proc R Soc Lond Ser A 160:268–282

  Article  MATH  Google Scholar 

• Bhattacharya RN, Ghosh JK (1978) On validity of the formal Edgeworth expansion. Ann Stat 6:434–451

  MATH  MathSciNet  Google Scholar 

• Boos DD, Brownie C (2004) Comparing variances and others measures of dispersion. Stat Sci 19:571–578

  Article  MATH  MathSciNet  Google Scholar 

• Box GEP (1953) Nonnormality and tests of variances. Biometrika 40:318–335

  MATH  MathSciNet  Google Scholar 

• Browne MW (1984) Asymptotically distribution-free methods for the analysis of covariance structures. Br J Math Stat Psychol 37:62–83

  MATH  MathSciNet  Google Scholar 

• Chao MT, Glaser RE (1978) The exact distribution of Bartlett’s test statistic for homogeniety of variances with unequal samples sizes. J Am Stat Assoc 73:422–426

  Article  MathSciNet  Google Scholar 

• Conover WJ, Johnson ME, Johnson MM (1981) A comparative study of test of homogeniety of variances: with applications to the outer continental shelf bindding data. Technometrics 23:351–361

  Article  Google Scholar 

• Dudewicz EJ, van der Muelen EC (1981) Entropy based tests of uniformity. J Am Stat Assoc 76:967–974

  Article  MATH  Google Scholar 

• Dyer DD, Keating JP (1980) On the determination of critical values for Bartlett’s test. J Am Stat Assoc 75:313–319

  Article  MATH  MathSciNet  Google Scholar 

• Fujikoshi Y, Ohmae M, Yanagihara H (1999) Asymptotic approximations of the null distribution of the one-way ANOVA test statistic under nonormality. J Japn Stat Soc 29:147–161

  MATH  MathSciNet  Google Scholar 

• Glaser RE (1976) Exact critical values for Bartlett’s test for homogeneity of variances. J Am Stat Assoc 71:488–490

  Article  MATH  MathSciNet  Google Scholar 

• Hall P (1992) The bootstrap and Edgeworth expansions. Springer, New York

  Google Scholar 

• Harrar SW, Gupta AK (2006) Asymptotic expansion of the null distribution of F-statistic for one-way ANOVA under non-normality. Ann Inst Stat Math (in Press)

• Kendall M, Stuart A, Ord JK (1987) Kendall’s advanced theory of statistics: distribution theory, 5th edn, vol 1. Oxford University Press, New York

  Google Scholar 

• Lehmann EL (1986) Testing statistical hypotheses. Springer, New York

  MATH  Google Scholar 

• Mardia KV (1970) Measures of multivariate skewness and kurtosis with applications. Biometrika 57: 519–530

  Article  MATH  MathSciNet  Google Scholar 

• Menéndez M, Morales D, Pardo L (1997) Maximum entropy principle and statistical inference on condensed ordered data. Stat Prob Lett 34:85–93

  Article  MATH  Google Scholar 

• Nayak TK (1985) On diversity measures based on entropy functions. Commun Stat Theory Methods 14: 203–215

  Article  MATH  MathSciNet  Google Scholar 

• Nayak TK (1986) Sampling distributions in analysis of diversity. Sankhya Ser B 48:1–9

  MATH  MathSciNet  Google Scholar 

• Neyman J, Pearson ES (1931) On the Problem of k-samples. Bull Acad Pol Sci Lett A, pp 460–481

• Pardo L, Salicrú M, Menéndez ML, Morales D (1995) A test for homogeneity of variances based on Shannon’s entropy. Metron 53:135–146

  MATH  MathSciNet  Google Scholar 

• Prescott P (1976) On a test for normality based on sample entropy. J R Stat Soc Ser B 38:254–256

  MATH  Google Scholar 

• Rao CR, Nayak TK (1985) Cross entropy, dissimilarity measures and characterization of quadratic entropy. IEEE Trans Info Theory 5:589–593

  Article  MathSciNet  Google Scholar 

• Shoemaker LH (2003) Fixing the F test for equal variances. Am Stat 57:105–114

  Article  MathSciNet  Google Scholar 

• Sugiura N, Nagao H (1969) On Bartlett’s test and Lehmann’s test for homogeneity of variances. Ann Math Stat 40:2018–2032

  MATH  MathSciNet  Google Scholar 

• Tonda T, Wakaki H (2003) Asymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a non-normal one-way ANOVA model. Hiroshima Math J 33:113–126

  MATH  MathSciNet  Google Scholar 

• Vasicek O (1976) A test for normality based on sample entropy. J R Stat Soc Ser B 38:54–59

  MATH  MathSciNet  Google Scholar 

• Yanagihara H (2000) Asymptotic expansion of the null distribution of the one-way ANOVA test statistic for heteroscedastic case under nonnormality. Commun Stat Theory Methods 29:463–476

  Article  MATH  MathSciNet  Google Scholar 

• Yanagihara H (2003) Asymptotic expansion of the null distribution of test statistic for linear hypothesis in non-normal linear model. J Multivariate Anal 84:222–246

  Article  MATH  MathSciNet  Google Scholar 

• Yanagihara H (2005) A family of estimators for multivariate kurtosis in a nonnormal linear regression model. J Multivariate Anal (in press)

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