A general framework for circular local likelihood regression
Authors: María Alonso Pena, Irène Gijbels and Rosa M. Crujeiras
Abstract: This article presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of a conditional characteristic is carried out nonparametrically, by maximizing the circular local likelihood, and the estimator is shown to be asymptotically normal. The problem of selecting the smoothing parameter is also addressed, as well as bias and variance computation. The performance of the estimation method in practice is studied through an extensive simulation study, where we cover the cases of Gaussian, Bernoulli, Poisson, and Gamma distributed responses. The generality of our approach is illustrated with several real-data examples from different fields. Supplementary materials for this article are available online.
Citation: Alonso-Pena, M., Gijbels, I. and Crujeiras, R.M. (2023). A general framework for circular local likelihood regression. To appear in Journal of the American Statistical Association.
Highlights:
General methodology for kernel regression estimation with circular covariates and general response
Proved the asymptotic normality of the estimator. Derived asymptotic bias and variance
Computed accurate approximations of bias and variance
Derived a new data-driven method for the selection of the smoothing parameter