= Equivariant estimator
{title2=$T(gy)=gT(y)$}
An estimator respects the <group action> if the displayed identity holds. If it takes values in the transformation <group> itself, normalization $T(y)^{-1}y$ is a <maximal invariant>: equivariance proves invariance, and equality of normalized samples reconstructs the transformation between them. For estimates in a homogeneous parameter space with a nontrivial stabilizer, normalization is defined only modulo that stabilizer; quotienting the remaining action is essential.
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