Quasi-likelihood estimation for semiparametric circular regression models

Motivated by the need for flexible and interpretable models to handle circular data, this paper introduces a semiparametric regression model for a circular response that can include both linear and circular covariates in its parametric and nonparametric components. Rather than imposing a particular parametric distribution on the error term, we adopt a circular quasi-likelihood function, which is useful when the underlying distribution is unknown. We discuss the asymptotic properties of the resulting estimators and a backfitting algorithm for model fitting. We evaluate the finite-sample performance of our proposal through simulations and illustrate its advantages for assessing the genetic effect on the migratory patterns of willow warblers. This offers new insights into how specific genomic elements can influence migratory behaviour.