On the relationship between partial sufficiency, invariance and conditional independence

J. Montanero, A. G. Nogales, J. A. Oyola & P. Perez
Several propositions that appear in a natural way in the literature on sufficiency and invariance, including the conditional independence of the invariant and the sufficient s-fields given its intersection, are adapted for partial sufficiency (in the sense of Fraser), and the relationship between them is studied.