DISTRIBUTIONS MINIMIZING FISHER INFORMATION FOR LOCATION IN KOLMOGOROV NEIGHBOURHOODS

EDEN K. H. WU AND P. S. CHAN

Department of Statistics, Chinese University of Hong Kong, Shatin, Hong Kong

(Received July 11, 1995; revised February 24, 1997)

Abstract. This paper is concerned with the problem of finding those distributions minimizing Fisher information for location over Kolmogorov neighbourhoods of distribution functions G satisfying certain mild conditions. The case when G is symmetric has been considered by quite a few authors. The general form of the solution is discussed. Furthermore we provide the solution of two asymmetric distributions, namely, the extreme value distribution and the Pearson’s type IV distribution.

Key words and phrases: Robust estimation of location, minimum Fisher information for location, extreme-value distribution, Pearson’s type IV distribution.