Huber-Sense Robust M-Estimation of a Scale Parameter, with Application to the Exponential Distribution.
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 Huber's 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 (-x/theta), 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1975
- Accession Number
- ADA014714
Entities
People
- Peter F Thall
- Robert Serfling
Organizations
- Florida State University