The affine type of distributions on the real line are represented as sequences of distributions of maximal invariants on spheres. It is shown that such a representation characterizes the affine type. A consistency condition is introduced, and it is shown that any sequence of maximal invariant distributions satisfying the condition is generated by some affine type on $\mathbf{R}$.
@article{1176346263,
author = {Small, Christopher G.},
title = {Characterization of Type from Maximal Invariant Spectra},
journal = {Ann. Statist.},
volume = {11},
number = {1},
year = {1983},
pages = { 979-983},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346263}
}
Small, Christopher G. Characterization of Type from Maximal Invariant Spectra. Ann. Statist., Tome 11 (1983) no. 1, pp. 979-983. http://gdmltest.u-ga.fr/item/1176346263/