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Generalized Leverage and its Applications
Author(s) -
Wei BoCheng,
Hu YueQing,
Fung WingKam
Publication year - 1998
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00086
Subject(s) - leverage (statistics) , mathematics , estimator , exponential family , econometrics , exponential function , generalized linear model , mathematical optimization , statistics , mathematical analysis
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