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Optimal confidence regions in GMANOVA
Author(s) -
Hooper Peter M.,
Yau Wai Kwok
Publication year - 1986
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315189
Subject(s) - mathematics , confidence interval , minimax , invariant (physics) , confidence region , confidence distribution , statistics , matrix (chemical analysis) , likelihood ratio test , cdf based nonparametric confidence interval , combinatorics , mathematical optimization , mathematical physics , materials science , composite material
Invariant confidence regions with smallest expected normalized volume are derived for a matrix of means of interest in the GMANOVA model, assuming only that the distribution of the matrix of residuals is left orthogonally invariant. Two invariance groups are considered, the usual full group and an amenable subgroup. A particular choice of the normalizing term leads to conditionally optimal confidence regions. Numerical results are given comparing the conditionally optimal fully invariant confidence region, which corresponds to the likelihood‐ratio test, with a conditionally minimax confidence region.