Unbiased Estimation Equation under f-Separable Bregman Distortion Measures
Unbiased Estimation Equation under f-Separable Bregman Distortion Measures
复制标题
f-可分离 Bregman 失真测度下的无偏估计方程
DOI：
10.1109/itw46852.2021.9457678
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Kazuho Watanabe
中科院分区：
文献类型：
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作者：
Masahiro Kobayashi;Kazuho Watanabe
利用单调增函数f和Bregman散度讨论了一类目标函数的无偏估计方程。函数f的选择给出了期望的性质，例如对离群值的鲁棒性。为了得到无偏估计方程，一般需要分析上难以处理的积分作为偏差校正项。在这项研究中，我们澄清了Bregman分歧，统计模型和函数f的组合，其中偏差校正项为零。专注于Mahalanobis和Itakura-Saito距离，我们提供了一个基本的现有结果的推广和刻画一类分布的正实数的尺度参数，其中包括伽玛分布作为一个特殊情况。我们讨论了潜在偏差最小化的可能性时，离群值的比例很大，这是由灭绝的偏差校正项。
We discuss unbiased estimation equations in a class of objective function using a monotonically increasing function f and Bregman divergence. The choice of the function f gives desirable properties such as robustness against outliers. In order to obtain unbiased estimation equations, analytically intractable integrals are generally required as bias correction terms. In this study, we clarify the combination of Bregman divergence, statistical model, and function f in which the bias correction term vanishes. Focusing on Mahalanobis and Itakura-Saito distances, we provide a generalization of fundamental existing results and characterize a class of distributions of positive reals with a scale parameter, which includes the gamma distribution as a special case. We discuss the possibility of latent bias minimization when the proportion of outliers is large, which is induced by the extinction of the bias correction term.