论文标题
收缩估算的特征平均值中的谎言组
Shrinkage Estimation of the Frechet Mean in Lie groups
论文作者
论文摘要
非欧盟人空间中的数据通常在科学和工程的许多领域都遇到。例如，在机器人技术中，态度传感器捕获了谎言群体的元素。最近，一些研究人员报道了在设计非线性空间中设计参数估计算法中谎言组的几何形状的方法。最大似然估计器（MLE）通常用于此类任务，并且在统计领域众所周知，斯坦因的收缩估计量在均值意义上以MLE为主导，假设观察结果来自正常人群。在本文中，我们提出了一个新颖的收缩估计量，用于属于谎言组的数据，特别是阿贝利安或紧凑的谎言组。本文提出的关键理论结果是：（i）Stein的引理及其对谎言组的证明以及（ii）所提出的收缩估计量在MLE上占主导地位的ABELIAN和紧凑型谎言组。我们介绍了拟议收缩估计量的主导地位以及收缩估计在多机器人定位中的应用的示例。
Data in non-Euclidean spaces are commonly encountered in many fields of Science and Engineering. For instance, in Robotics, attitude sensors capture orientation which is an element of a Lie group. In the recent past, several researchers have reported methods that take into account the geometry of Lie Groups in designing parameter estimation algorithms in nonlinear spaces. Maximum likelihood estimators (MLE) are quite commonly used for such tasks and it is well known in the field of statistics that Stein's shrinkage estimators dominate the MLE in a mean-squared sense assuming the observations are from a normal population. In this paper, we present a novel shrinkage estimator for data residing in Lie groups, specifically, abelian or compact Lie groups. The key theoretical results presented in this paper are: (i) Stein's Lemma and its proof for Lie groups and, (ii) proof of dominance of the proposed shrinkage estimator over MLE for abelian and compact Lie groups. We present examples of simulation studies of the dominance of the proposed shrinkage estimator and an application of shrinkage estimation to multiple-robot localization.
