Semiparametric regression for circular responsewith application in ecology

Abstract

A regression model for a circular response variabledepending on a linear or a circular predictor is pre-sented in this paper. The conditional density belongsto a parametric flexible family that allows for asymme-try and varying peakedness around the modal direction.The modal direction and concentration depend on thecovariate and are nonparametrically modeled via localpolynomial fitting with a kernel weight. The asymp-totic normality of the estimators for the conditionalmodal direction and concentration is established. Fur-thermore, from these theoretical results, the expressionof the optimal smoothing parameter and a proposeddata-driven estimator are derived. An application con-cerns the orientation of migratory birds according to theflight altitude and the wind direction.