This paper 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.

翻译：本文提出了一个用于估计含圆形协变量的回归模型的一般框架，其中响应变量在给定协变量条件下的条件分布可通过参数模型进行设定。通过最大化圆形局部似然，实现了条件特征的非参数估计，并证明了该估计量是渐近正态的。此外，本文还解决了平滑参数的选择问题，以及偏差和方差的计算。通过广泛的数值模拟研究，评估了该估计方法在实际应用中的性能，涵盖了响应变量服从高斯、伯努利、泊松和伽马分布的情况。来自不同领域的多个真实数据案例，充分展示了我们方法的普适性。