Acta Mathematicae Applicatae Sinica

, Volume 10, Issue 4, pp 387–400 | Cite as

An analysis of a multivariate two-way model with interaction and no replication

  • Guo Dawei 
Article
  • 39 Downloads

Abstract

In this paper, we consider the problem of testing the hypothesis of no interaction in the multivariate two-way classification model with one observation per cell. If the error covariance matrix is unknown, we suggest pseudo-maximum likelihood estimation (PMLE) of the parameters and give the invariant test for the hypothesis of no interaction. Further, we develop also some tests for the case of an unknown diagonal positive definite error covariance matrix.

Key words

Analysis of variance interaction pseudo-maximum likelihood estimate maximal invariant invariant test 

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References

  1. [1]
    Guo Dawei. Tests for the Hypothesis of a Class of No Interaction in the Multivariate Two-way Classification Model.Acta Scientiarum Naturalium Universitatis Jilinesis, 1983, 3: 15–27.Google Scholar
  2. [2]
    Johnson, D.E. and Graybill, F.A. An Analysis of a Two-Way Model with Interaction and No Replication.J. Amer. Statist. Assoc., 1972, 67: 862–868.MATHMathSciNetGoogle Scholar
  3. [3]
    Krishnaiah, P.R. and Schuurmann, F.J. On the Evaluation of Some Distribution that Aries in Simultaneous Tests for the Equality of the Latent roots of the Covariance Matrix.J. Multivariate Anal., 1974, 4: 265–282.CrossRefMathSciNetMATHGoogle Scholar
  4. [4]
    Corsten, L.C.A. and Van Eijnsbergen, A.C. Multiplicative Effects in Two-way Analysis of Variance.Statistics Neerlandica, 1972, 26: 61–68.CrossRefGoogle Scholar
  5. [5]
    Krishnaiah, P.R. Developments in Statistics, Vol. 1, p. 135–169. Academic Press, New York, 1978.MATHGoogle Scholar
  6. [6]
    Pillai, K.C.S. and Nagarsenker, B.N. On the Distribution of the Sphericity Test Criterion in Classical and Complex Normal Populations Having Unknown Covariance Matrix.Ann. Math. Statist., 1971, 42: 764–767.MATHGoogle Scholar
  7. [7]
    Krishnaiah, P.R. Computations of Some Multivariate Distributions. In Handbook of Statistics 1, North-Holland, Amsterdam, 1980.Google Scholar
  8. [8]
    Rao, C.R. Linear Statistical Inference and its Applications. 2nd Ed., John Wiley & Sons, 1973.Google Scholar
  9. [9]
    Giri, N.C. Multivariate Statistical Inference. Academic Press, New York, San Farncisco, London, 1977.MATHGoogle Scholar
  10. [10]
    Muirhead, R.J. Aspects of Multivariate Statistical Theory. John Wiley & Sons, INC., New York, 1982.MATHGoogle Scholar
  11. [11]
    Krishnaiah, P.R. On Generalized Multivariate Gamma Type Distribution and Their Applications in Reliability. Proc. Conf. Theory and Appl. of Reliability with Emphasis on Bayesian and Nonparametric Methods (I.N. Shimi and C.P. Tsokos, eds.), Academic Press, New York, 1977.Google Scholar
  12. [12]
    Krishnaiah, P.R. and Waikar, V.B. On the Distribution of a Linear Combination of Correlated Quadratic Forms.Commun. Statist., 1973, 1: 371–380.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Fujikoshi, Y. Asymptotic expansions of the Distributions of Test Statistics in Multivariate Analysis.J. Sci. Hiroshima Univ. (Ser. A-I), 1970, 34: 73–144.MATHMathSciNetGoogle Scholar

Copyright information

© Science Press 1994

Authors and Affiliations

  • Guo Dawei 
    • 1
  1. 1.Department of MathematicsAnhui Normal UniversityWuhuChina

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