A flexible regression model for circular responses
We introduce a flexible regression model designed for circular response variables, accommodating both linear and circular predictors. Unlike traditional circular regression models, our approach utilizes a parametric density family that can adapt to asymmetry and varying levels of concentration. The modal direction and dispersion parameters are estimated nonparametrically through local polynomial fitting with kernel-based weighting. We establish the asymptotic properties of these estimators and derive an optimal smoothing parameter with a data-driven selection method. The practical utility of the model is demonstrated through an application in birds migration, where we examine how flight orientation varies with altitude and wind direction.
Keywords: Directional Statistics Flexible Modeling Local Likelihood Modal Direction Regression