Abstract

Logistic regression is the most widely used statistical method for linear discriminant analysis. In many applications, however, we can only observe the possibly mislabeled response, and directly fitting logistic regression model can cause serious bias. A commonly used solution is to fit mislabel logistic regression, which models the success probability under the consideration of mislabeling. Although mislabel logistic regression is demonstrated to be useful, its success relies on the correctness of an extra modeling for mislabel probability, which is rarely known in practice. Another branch of method stays with the conventional logistic regression model, but adopts a robust M-estimation by down-weighting suspected subjects. To en- sure consistency, a bias correction term is subtracted from the estimating equation, but may increase the difficulty of interpretation. In this work, we propose a new robust γ-logistic regression that avoids modeling the mislabeling probability, by the virtue of γ-divergence. Another merit is that γ-logistic uses a different bias correction scheme, which results in a weighted expression of the estimating equation. These properties make γ-logistic more robust in model fitting, more intuitive in explanation, and easier in implementation. 

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