Invariance, almost-invariance and sufficiency


  • Agustin G. Nogales Universidad de Estremadura
  • José A. Oyola Universidad de Estremadura
  • Paloma Perez Universidad de Estremadura



This 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.