A general framework for circular local likelihood regression

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.

本文提出了一种面向带循环协变量（circular covariates）的回归模型估计的通用框架，其中响应变量给定协变量时的条件分布可通过参数模型进行设定。本文采用非参数方法，通过最大化循环局部似然（circular local likelihood）估计条件特征，并证明该估计量服从渐近正态分布。本文还探讨了平滑参数（smoothing parameter）的选择问题，并给出了偏差与方差的计算方法。通过覆盖高斯、伯努利、泊松及伽马分布响应变量的大规模模拟实验，本文对所提估计方法的实际性能展开了研究。此外，本文借助多个来自不同领域的实际数据示例，验证了所提方法的通用性。