Invariance, almost-invariance and sufficiency
AbstractThis paper is concerned with the relationship between sufficiency, invariance and conditional indipendence. Given a sufficient [sigma]-field, two results are obtained about independence and conditional independence of it and the almost invariant [sigma]-field. Moreover, it includes a rigorous proof of a stronger result than a Stein theorem about sufficiency and invariance in its version for statistics and in the discrete case. Somewhat of a strange condition is used to prove this theorem in its original form; several results are given here to clarify it.
How to Cite
Nogales, A. G., Oyola, J. A., & Perez, P. (2000). Invariance, almost-invariance and sufficiency. Statistica, 60(2), 277–286. https://doi.org/10.6092/issn.1973-2201/6940