Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The “closest” estimates of statistical parameters

E. J. G. Pitmana1

a1 Hobart, Tasmania

A definition of “closer” and “closest” as applied to estimates of statistical parameters is given, and it is shown that we can sometimes prove that estimates properly derived from sufficient statistics are the closest possible.

The scaling of a gamma distribution, and the location and scaling of an exponential distribution and of a rectangular distribution are discussed in detail, and the closest estimates of the parameters obtained.

(Received September 19 1936)

(Accepted March 08 1937)