A statistical prediction problem invariant under a certain group of transformations is considered. Under several assumptions it is shown that the best invariant predictor is obtained by using the invariant measure on the group. This result is an extension of that of Hora and Buehler.
Yoshikazu Takada. "A Comment on Best Invariant Predictors." Ann. Statist. 10 (3) 971 - 978, September, 1982. https://doi.org/10.1214/aos/1176345887