Advanced search
Publication Cover
American Journal of Mathematical and Management Sciences Volume 8, 1988 - Issue 1-2
Submit an article Journal homepage
10
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Asymptotic Expansions of the Non-Null Distribution of the Likelihood Ratio Criterion for Multisample Sphericity

Panagis G. MoschopoulosDepartment of MathematicsSouthwest Missouri State UniversitySpringfield, Missouri65804
Pages 135-163 | Published online: 14 Aug 2013

  • AndersonT.W. (1984). An Introduction to Multivariate Statistical Analysis. John Wiley & Sons, Inc., New York.
  • BoxG.E.P. (1949). A general distribution theory for a class of likelihood criteria. Biometrika, 36, 317–346.
  • ErdelyiA., MagnusW., OberhettingerF., and TricomiF.G. (1953). Higher Transcendental Functions. Vol. I. McGraw-Hill, New York.
  • FisherR.A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179–188.
  • HuynhH. and FeldtL.S. (1970). Conditions under which mean square ratios in repeated measurements designs have exact F–distributions. Journal of the American Statistical Association, 65, 1582–1585.
  • KhatriC.G. and SrivastavaM.S. (1971). On exact non–null distributions of likelihood ratio criteria for sphericity test and equality of two covariance matrices. Sankhya, 33A, 201–206.
  • KhatriC.G. and SrivastavaM.S. (1974). Asymptotic expansions of the non–null distributions of likelihood ratio criteria for covariance matrices. Annals of Statistics, 2, 109–117.
  • LukeY.L. (1969). The Special Functions and Their Approximations. Vol. I. Academic Press, New York.
  • MathaiA.M. (1984). On the hypothesis of multisample sphericity. Soviet Journal of Mathematics (ZAPISKI NAUCHNYKH SEMINAROV), LOMI 136, pp. 153–161. Also Technical Report No. 83–23, Department of Mathematics, McGill University, MontrealCanada.
  • MauchlyJ.W. (1940). Significance test for sphericity of a normal n–variate distribution. Annals of Mathematical Statistics, 11, 204–209.
  • MendozaJ. L. (1980). A significance test for multisample sphericity. Psvchometrika, 45, 495–498.
  • MorrisonD.F. (1976). Multivariate Statistical Methods. McGraw-Hill Book Co., New York.
  • NagaoH. (1970). Asymptotic expansions of some test criteria for homogeneity of variances and covariance matrices from normal populations. Journal of Sciences, Hiroshima University. Series A, Part I, Volume 34, 153–247.
  • NagaoH. (1973). Asymptotic expansions of the distributions of Bartlett's test and sphericity test under local alternatives. Annals of the Institute of Statistical Mathematics, 25, 407–422.
  • SugiuraN. (1969). Asymptotic expansions of the distributions of the likelihood ratio criteria for covariance matrix. Annals of Mathematical Statistics, 40, 2051–2063.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.