Nonparametric estimators of a regression function with circular response and \({\mathbb {R}}^d\)-valued predictor are considered in this work. Local polynomial estimators are proposed and studied. Expressions for the asymptotic conditional bias and variance of these estimators are derived, and some guidelines to select asymptotically optimal local bandwidth matrices are also provided. The finite sample behavior of the proposed estimators is assessed through simulations, and their performance is also illustrated with a real data set.

中文翻译：

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循环响应的非参数多元回归估计

在这项工作中考虑了具有循环响应和\（{\ mathbb {R}} ^ d \）值的预测变量的回归函数的非参数估计量。提出并研究了局部多项式估计。推导了这些估计量的渐进条件偏差和方差的表达式，并提供了一些选择渐近最优局部带宽矩阵的准则。拟议估计量的有限样本行为通过模拟进行评估，并且其性能也通过真实数据集进行了说明。