Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M ‐estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non‐linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results