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Activity Number: 244
Type: Contributed
Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Epidemiology
Abstract #311364 View Presentation
Title: Local Likelihood-Based Estimation for Quantile Classification in Binary Regression Models
Author(s): John Rice*+ and Jeremy Taylor
Companies: University of Michigan and University of Michigan
Keywords: binary classification ; local likelihood ; logistic regression ; asymmetric loss ; robust estimation
Abstract:

One common use of binary response regression methods is classification based on an arbitrary probability threshold dictated by the particular application. Since this is given to us a priori, it is sensible to incorporate the threshold into our estimation procedure. Specifically, for the linear logistic model, we solve a set of locally weighted score equations, using a kernel-like weight function centered at the threshold. The bandwidth for the weight function is selected by cross validation of a novel class of hybrid loss functions that combine classification error and a continuous measure of divergence between observed and fitted values. Although inspired by local likelihood methodology, this work shares more in common with robust estimation, but differs from previous approaches in both areas in its focus on prediction, specifically classification into high- and low-risk groups. Simulation results are given showing the reduction in error rates that can be obtained with this method when compared with maximum likelihood estimation under certain forms of model misspecification. Analysis of a melanoma data set is presented to illustrate the use of the method in practice.


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