Bias of maximum likelihood estimators of the response standard deviation in regression

Abstract

The bias of maximum likelihood estimators of the standard deviation of the response in location/scale regression models is considered. Results are obtained for a very wide family of densities for the response variable. These are used to propose point estimators with improved mean square error properties and to demonstrate the importance of bias correction in statistical inference when samples are moderately small.

Keywords:

• multiple regression
• standard deviation of response
• maximum likelihood estimation
• bias