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Invariant estimates of the shift for distributions on finite groups

V. M. Maksimov<sup>ab

a</sup> Kaliningrad State University
^b Institute of Chemical Physics of the USSR Academy of Sciences

Abstract: Let $\{\mu\alpha\}$ be a family of measures on a finite group $G$ where $\mu$ is a measure on $G$ and $\alpha\in G$. The measure $\mu\alpha$ is said to be obtained from $\mu$ by shift $\alpha$.
In the paper, invariant estimates $f(x)$, $x$ being a sample $(x_1,\dots,x_n)$ from the distribution $\mu\alpha$ with a known $\mu$, for the shift $\alpha$ are constructed, i.e. such estimates that $\varphi(f(x))=f(\varphi(x))$ for any automorphism $\varphi$.

Received: 26.07.1973

 English version: Theory of Probability and its Applications, 1975, 20:1, 69–82

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