论文标题
自适应扭曲的内核估计非参数回归具有圆形响应
Adaptive warped kernel estimation for nonparametric regression with circular responses
论文作者
论文摘要
在本文中，我们处理循环数据的非参数回归，这意味着观测值是由位于单位圆上的点表示。我们提出了一个内核估计过程，并选择了带宽参数的数据驱动选择。为此，我们使用翘曲策略与Goldenshluger-Lepski型估计器相结合。为了研究我们的方法论的最佳性，我们通过建立上限和下限来考虑最小值设置并证明我们的过程几乎是各向异性持有人的功能类别的最佳选择，以进行点上的估计。获得的速率还揭示了循环响应回归的特定性质。最后，进行了数值研究，说明了我们方法的良好表现。
In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth parameter. For this purpose, we use a warping strategy combined with a Goldenshluger-Lepski type estimator. To study optimality of our methodology, we consider the minimax setting and prove, by establishing upper and lower bounds, that our procedure is nearly optimal on anisotropic Holder classes of functions for pointwise estimation. The obtained rates also reveal the specific nature of regression for circular responses. Finally, a numerical study is conducted, illustrating the good performances of our approach.
