Locally minimax test of independence in elliptically symmetrical distributions with additional observations |
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| Authors: | N. Giri M. Behara P. Banerjee |
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| Affiliation: | (1) Dépt. de Math. et Stat., Université de Montréal, P.O. Box 6/28 Station A, H3C 3J7 Montreal, Quebec, Canada;(2) Dept. of Math., McMaster University, Hamilton, Ontario, Canada;(3) Dept. of Math. & Stat., Univ. of New-Burnswick, Fredricton, New-Burnswick, Canada |
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| Abstract: | Summary LetX=(X ij )=(X 1, ...,X n )’,X’ i =(X i1, ...,X ip )’,i=1,2, ...,n be a matrix having a multivariate elliptical distribution depending on a convex functionq with parameters, 0,σ. Let ϱ2=ϱ 2 -2 be the squared multiple correlation coefficient between the first and the remainingp 2+p 3=p−1 components of eachX i . We have considered here the problem of testingH 0:ϱ2=0 against the alternativesH 1:ϱ 1 -2 =0, ϱ 2 -2 >0 on the basis ofX andn 1 additional observationsY 1 (n 1×1) on the first component,n 2 observationsY 2(n 2×p 2) on the followingp 2 components andn 3 additional observationsY 3(n 3×p 3) on the lastp 3 components and we have derived here the locally minimax test ofH 0 againstH 1 when ϱ 2 -2 →0 for a givenq. This test, in general, depends on the choice ofq of the familyQ of elliptically symmetrical distributions and it is not optimality robust forQ. |
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| Keywords: | Elliptically symmetric distributions invariance locally best invariant test locally minimax test optimality robust. |
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