Parameter Selection of Robust Weighted SCAD Model Under Density Power Divergence

Logistic regression is an important classification model in regression analysis, but its ability to deal with contaminated data is poor. To solve this problem, this paper extends the logistic loss function which based on maximum likelihood reasoning robustly, and constructs the logic DPD Loss function in the form of density power divergence. In the current research on regression models related to density power divergence, the penalty terms of the model are all non-concave penalties. This paper uses the non-convex penalty function SCAD as the penalty term to build a new Logistic regression model based on DPD, and gives the theoretical proof of the robustness of the model under the contaminated data. Through data simulation, we have confirmed that the SCAD model under density power divergence has strong contaminated data processing ability, and found a suitable selection method for important parameters in the model.