# Accession Number:

## AD1028390

# Title:

## Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution

# Descriptive Note:

## Conference Paper

# Corporate Author:

## STANFORD UNIVERSITY STANFORD United States

# Personal Author(s):

# Report Date:

## 1956-01-01

# Pagination or Media Count:

## 11.0

# Abstract:

If one observes the real random variables Xi, Xn independently normally distributed with unknown means xi...x in and variance 1, it is customary to estimate xi by Xi. If the loss is the sum of squares of the errors, this estimator is admissible for n or equal to 2, but inadmissible for n more than or equal to 3. Since the usual estimator is best among those which transform correctly under translation, any admissible estimator for n equals more than or equal to 3 involves an arbitrary choice. While the results of this paper are not in a form suitable for immediate practical application, the possible improvement over the usual estimator seems to be large enough to be of practical importance if n is large.

# Subject Categories:

- Statistics and Probability