Professor Yongli Sang

University of Louisiana at Lafayette

Abstract: Canonical correlation analysis (CCA) is a classical tool for measuring the dependence between two random vectors, X ∈ ℝ^p and Y ∈ ℝ^q. When X and Y are functional curves, functional canonical correlation analysis (FCCA) is used to characterize the linear association between random functions.

In this project, we develop a new FCCA framework for discriminant analysis when the response variable Y is categorical. The proposed dependence measure is constructed by extending the categorical Gini correlation to the functional setting, allowing us to quantify the association between a functional predictor and a categorical response. We establish theoretical properties of the proposed estimator, including its consistency.

Through extensive simulation studies, we demonstrate that the proposed method provides accurate and stable estimation of the dependence structure and performs well in discriminant analysis. The practical utility of the proposed approach is further illustrated through a real data example in which a k-sample testing problem is considered.