Robust Statistical Methods for the Functional Logistic Model

Abstract

Over the last decade or so, a lot of interest has emerged in the field of functional data analysis. This interest spans from a broad spectrum of fields such as brain imaging studies, bio-metrics, genetics, e-commerce and computer science. Statistical tools, models and methods, whose strength is in recognizing this structural aspect of data are being discussed and developed; ranging from functional linear regression, functional ANOVA, functional principal component analysis and functional outlier detection. In this work, we discuss statistical methods for the functional logistic regression model; a model where the response is binary and the covariate(s) functional. Essentially, we consider ways that allow for the parameter estimator to be resistant to outliers, in addition to eliminating multicollinearity and high dimensional problems; issues which are inherent with functional data. The methods include robust techniques of estimating the parameter function for the model as well as diagnostic measures to assess the fit of the model. Two estimation approaches are discussed; the first one makes use of robust principal component estimation techniques and the second one uses a robust penalization approach. Results from a simulation study and a real world example are also presented to illustrate the performance of the proposed estimators.