A Nonparametric Method of Parameter Estimation in Logistic Regression Under Case-Control Study

• Activity Number: 262
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Pei Geng*
• Companies: Michigan State University
• Keywords: Logistic Regression ; Nonparametric method ; Kernel density estimation ; Case control study

Abstract

In logistic regression analysis, the response is binary. Because of the Bayesian rule, the logistic regression is equivalent to the case-control study. The majority of the case-control study are based on semi-parametric likelihood procedure. Here we propose a nonparametric method to estimate the parameters in the logistic regression. Observing the pattern between the densities of the two groups, if the case-control framework is appropriate, the log ratio of the two densities is a linear function of covariates. one can obtain nonparametric density estimators for each group such as kernel density estimators. Then the integrated square distance is defined between the estimated log ratio and the linear function of covariates. One can obtain the parameter estimators by minimizing the integrated square distance. Consistency and asymptotic normality of the underlying parameter estimators are derived. Based on the integrated square distance, one can also test the validity of the logistic regression.