Elliptically contoured model and factorization of Wilks' $ \Lambda$: noncentral case

Authors

  • A. K. Gupta
  • D. G. Kabe

DOI:

https://doi.org/10.5556/j.tkjm.31.2000.395

Abstract

Kshirsagar in a series of papers, see e.g., Kshirsagar (1964, 1971), McHenry and Kshirsagar (1977), factorizes Wilks' $ \Lambda$ into a number of factors and finds the independent central multivariate beta densities of these factors. These factors are the Wilks' likelihood ratio test criteria for testing goodness of fit of certain canonical variables. Essentially the factors of Wilks' $ \Lambda$ are the factors of the determinants of certain multivariate beta distributed matrices. The Bartlett decompositions of the underlying multivariate beta distribution into independent factors, determine the distributions of these factors. The present paper generalizes Kshirsagar's (1971) normal central distribution theory to elliptically contoured model noncentral distribution theory, showing that Kshirsagar's (1971) nonnull normal theory is nonnull robust for elliptically contoured model.

Author Biographies

A. K. Gupta

Dept. of Math. Stat., Bowling Green State University, Bowling Green, OH 43403, U.S.A.

D. G. Kabe

Dept. of Math. Comp. Sci., St. , Halifax, NS Canada B3H3C3.

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Published

2000-09-30

How to Cite

Gupta, A. K., & Kabe, D. G. (2000). Elliptically contoured model and factorization of Wilks’ $ \Lambda$: noncentral case. Tamkang Journal of Mathematics, 31(3), 213-222. https://doi.org/10.5556/j.tkjm.31.2000.395

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Papers