A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis

Test

Volumn 20, Issue 1, 2011, Pages 180-203

  Marques, Filipe J ^a   Coelho, Carlos A ^a   Arnold, Barry C ^b  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Generalized Integer Gamma distribution; Generalized Near Integer Gamma distribution; Independence test; Mixtures; Sphericity test; Wilks lambda statistic

Indexed keywords

EID: 79955784230     PISSN: 11330686     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11749-010-0193-3     Document Type: Article

References (22)

1. Anderson TW (2003) An introduction to multivariate statistical analysis, 3rd edn. Wiley, New York.
2. Anderson TW, Fang K-T (1990) Inference in multivariate elliptically contoured distributions based on maximum likelihood. In: Fang K-T, Anderson TW (eds) Statistical inference in elliptically contoured and related distributions, pp 201-216.
3. Anderson TW, Fang K-T, Hsu H (1986) Maximum-likelihood estimates and likelihood-ratio criteria for multivariate elliptically contoured distributions. Can J Stat 14: 55-59.
4. Aslam S, Rocke DM (2005) A robust testing procedure for the equality of covariance matrices. Comput Stat Data Anal 49: 863-874.
5. Berry A (1941) The accuracy of the Gaussian approximation to the sum of independent variates. Trans Am Math Soc 49: 122-136.
6. Coelho CA (1992). Generalized canonical analysis. PhD thesis, The University of Michigan, Ann Arbor, MI.
7. Coelho CA (1998) The Generalized Integer Gamma distribution-a basis for distributions in Multivariate Statistics. J Multivar Anal 64: 86-102.
8. Coelho CA (2004) The Generalized Near-Integer Gamma distribution: a basis for 'near-exact' approximations to the distributions of statistics which are the product of an odd number of independent Beta random variables. J Multivar Anal 89: 191-218.
9. Coelho CA (2007) The wrapped Gamma distribution and wrapped sums and linear combinations of independent Gamma and Laplace distributions. J Stat Theory Practice 1: 1-29.
10. Coelho CA, Marques FJ (2009a) The advantage of decomposing elaborate hypotheses on covariance matrices into conditionally independent hypotheses in building near-exact distributions for the test statistics. Linear Algebra Appl 430: 2592-2606.
11. Coelho CA, Marques FJ (2009b). Near-exact distributions for the likelihood ratio test statistic for testing equality of several variance-covariance matrices (revisited). The New University of Lisbon, Mathematics Department, technical report #9/2009, submitted for publication. http://www. dmat. fct. unl. pt/fct/servlet/DownloadFile?file=1162& sub=investiga& modo=prepub.
12. Coelho CA, Marques FJ (2010) Near-exact distributions for the independence and sphericity likelihood ratio test statistics. J Multivar Anal 101: 583-593.
13. Coelho CA, Alberto RP, Grilo LM (2006) A mixture of Generalized Integer Gamma distributions as the exact distribution of the product of an odd number of independent Beta random variables: applications. J Interdiscip Math 9: 229-248.
14. Esseen C-G (1945) Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law. Acta Math 77: 1-125.
15. Hsieh HK (1979) On asymptotic optimality of likelihood ratio tests for multivariate normal distributions. Ann Stat 7: 592-598.
16. Hwang H-K (1998) On convergence rates in the central limit theorems for combinatorial structures. Eur J Combin 19: 329-343.
17. Jensen DR, Good IJ (1981) Invariant distributions associated with matrix laws under structural symmetry. J R Stat Soc Ser B 43: 327-332.
18. Kariya T (1981) Robustness of multivariate tests. Ann Stat 9: 1267-1275.
19. Kshirsagar AM (1972) Multivariate analysis. Dekker, New York.
20. Loève M (1977) Probability theory, 4th edn, vol I. Springer, New York.
21. Marques FJ, Coelho CA (2008) Near-exact distributions for the sphericity likelihood ratio test statistic. J Stat Plan Inference 138: 726-741.
22. Mauchly JW (1940) Significance test for sphericity of a normal n-variate distribution. Ann Math Stat 11: 204-209.