Di Marzio Marco, Fensore Stefania, Panzera Agnese, Taylor Charles C
DMQTE, Università di Chieti-Pescara, Viale Pindaro 42, Pescara, Italy.
DiSIA, Università di Firenze, Viale Morgagni 59, Firenze, Italy.
Biometrics. 2022 Mar;78(1):248-260. doi: 10.1111/biom.13431. Epub 2021 Feb 9.
Until now the problem of estimating circular densities when data are observed with errors has been mainly treated by Fourier series methods. We propose kernel-based estimators exhibiting simple construction and easy implementation. Specifically, we consider three different approaches: the first one is based on the equivalence between kernel estimators using data corrupted with different levels of error. This proposal appears to be totally unexplored, despite its potential for application also in the Euclidean setting. The second approach relies on estimators whose weight functions are circular deconvolution kernels. Due to the periodicity of the involved densities, it requires ad hoc mathematical tools. Finally, the third one is based on the idea of correcting extra bias of kernel estimators which use contaminated data and is essentially an adaptation of the standard theory to the circular case. For all the proposed estimators, we derive asymptotic properties, provide some simulation results, and also discuss some possible generalizations and extensions. Real data case studies are also included.
到目前为止，当数据存在观测误差时，估计圆形密度的问题主要通过傅里叶级数方法来处理。我们提出了基于核的估计器，其构造简单且易于实现。具体来说，我们考虑三种不同的方法：第一种基于使用不同误差水平的损坏数据的核估计器之间的等价性。尽管该方法在欧几里得环境中也有应用潜力，但似乎完全未被探索过。第二种方法依赖于其权重函数为圆形反卷积核的估计器。由于所涉及密度的周期性，它需要特殊的数学工具。最后，第三种方法基于校正使用受污染数据的核估计器的额外偏差的思想，本质上是将标准理论应用于圆形情况。对于所有提出的估计器，我们推导了渐近性质，提供了一些模拟结果，并讨论了一些可能的推广和扩展。还包括实际数据案例研究。
