  Logistic regression is among the most widely used statistical methods for
linear discriminant analysis. In many applications, we only observe possibly
mislabeled responses. Fitting a conventional logistic regression can then lead
to biased estimation. One common resolution is to fit a mislabel logistic
regression model, which takes into consideration of mislabeled responses.
Another common method is to adopt a robust M-estimation by down-weighting
suspected instances. In this work, we propose a new robust mislabel logistic
regression based on gamma-divergence. Our proposal possesses two advantageous
features: (1) It does not need to model the mislabel probabilities. (2) The
minimum gamma-divergence estimation leads to a weighted estimating equation
without the need to subtract any bias correction term, i.e., it is
automatically bias corrected. These properties make the proposed gamma-logistic
regression more robust in model fitting and more intuitive for model
interpretation through a simple weighting scheme. Our method is also easy to
implement, and two types of algorithms are included. Simulation and real data
application results are presented to demonstrate the performance of
gamma-logistic.
