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Logistic discrimination using robust estimators: An influence function approach
Author(s) -
Croux Christophe,
Haesbroeck Gentiane,
Joossens Kristel
Publication year - 2008
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.5550360114
Subject(s) - logistic regression , estimator , statistics , mathematics , logistic function , function (biology) , set (abstract data type) , econometrics , logistic distribution , plot (graphics) , pattern recognition (psychology) , computer science , artificial intelligence , evolutionary biology , biology , programming language
Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set and these might affect the estimated model and the associated classification error rate. In this paper, the authors study the effect of observations in the training sample on the error rate by deriving influence functions. They obtain a general expression for the influence function of the error rate, and they compute it for the maximum likelihood estimator as well as for several robust logistic discrimination procedures. Besides being of interest in their own right, the influence functions are also used to derive asymptotic classification efficiencies of different logistic discrimination rules. The authors also show how influential points can be detected by means of a diagnostic plot based on the values of the influence function