Semiparametric regression for circular response with application in ecology

ABSTRACT A regression model for a circular response variable depending on a linear or a circular predictor is presented in this paper. The conditional density belongs to a parametric flexible family that allows for asymmetry and varying peakedness around the modal direction. The modal direction and concentration depend on the covariate and are nonparametrically modeled via local polynomial fitting with a kernel weight. The asymptotic normality of the estimators for the conditional modal direction and concentration is established. Furthermore, from these theoretical results, the expression of the optimal smoothing parameter and a proposed data‐driven estimator are derived. An application concerns the orientation of migratory birds according to the flight altitude and the wind direction.