WITHDRAWN: Random Point Impact Model for Functional Logistic Regression

• Author(s): Wei Xiong
• Keywords: functional logistic regression ; Brownian motion ; Expectation-Maximization ; misspecification ; latent variable ; mixture model

Abstract

In common functional logistic regression models, the functional predictor is assumed to be smooth. The influence of the predictor process on the scalar response is further assumed to be spread across its support. We consider an alternative model where the predictor process is assumed to have similar behavior to a Brownian motion. It is associated with the scalar response only via its value at a specific but unknown "time point". We allow for individual heterogeneity of such sensitive time point by assuming it is random. An EM-based maximum likelihood method is developed to estimate the location parameter of the sensitive point as well as the regression coefficients. Simulation studies confirm the proposed method by investigating distributions of the estimators. We also studied how these estimators are affected when the dispersion parameter of the sensitive time point is misspecified.