Canadian Journal of Statistics

Optimal confidence regions in GMANOVA

Journal Article

Abstract

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.

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