AISM 53, 427-435
© 2001 ISM

Information inequalities in a family of uniform distributions

Masafumi Akahira1 and Kei Takeuchi2

1Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan
2Faculty of International Studies, Meiji-Gakuin University, Kamikurata-cho 1598, Totsuka-ku, Yokohama 244-0816, Japan

(Received June 2, 1999; revised January 21, 2000)

Abstract.    For a family of uniform distributions, it is shown that for any small $\e>0$ the average mean squared error (MSE) of any estimator in the interval of $\t$ values of length $\e$ and centered at $\t_0$ can not be smaller than that of the midrange up to the order $o(n^{-2})$ as the size $n$ of sample tends to infinity. The asymptotic lower bound for the average MSE is also shown to be sharp.

Key words and phrases:    Best location equivariant estimator, average mean squared error, sufficient statistic.

Source (TeX, DVI )