Estimable group effects for strongly correlated variables in linear models

Abstract

It is well known that parameters for strongly correlated predictor variables in a linear model cannot be accurately estimated. We look for linear combinations of these parameters that can be. Under a uniform model, we find such linear combinations in a neighborhood of a simple variability weighted average of these parameters. Surprisingly, this variability weighted average is more accurately estimated when the variables are more strongly correlated, and it is the only linear combination with this property. It can be easily computed for strongly correlated predictor variables in all linear models and has applications in inference and estimation concerning parameters of such variables.