# Accession Number:

## ADA014714

# Title:

## Huber-Sense Robust M-Estimation of a Scale Parameter, with Application to the Exponential Distribution.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1975-07-01

# Pagination or Media Count:

## 22.0

# Abstract:

A theory of robust M-estimation of a location parameter was developed by Huber 1964 and applied to estimation of the mean of a normal distribution. This theory is applicable to the problem of robust estimation of a scale parameter, since nonnegative data X having scale parameter theta may be transformed by y log x into data Y having location parameter log theta. Equivalently, in the present article the authors reformulate Hubers location parameter results in the scale parameter content--that is transform the theorems instead of the data--and we the authors apply the results in connection with the problem of robust estimation of the parameter theta of the exponential distribution, 1 - exp -xtheta, x 0. Whereas the maximum likelihood estimator of theta is the sample mean, the robust M-estimator, which is the solution of a minimax problem based on the asymptotic variance criterion, turns out to be a type of Winsorized mean. Numerical illustration is provided using a data set of Proschan 1963 consisting of the time intervals between successive failures of the air conditioning systems of a fleet of jet airplanes.

# Subject Categories:

- Statistics and Probability