论文标题
$ f $分离的布雷格曼失真措施下的公正估计方程
Unbiased Estimation Equation under $f$-Separable Bregman Distortion Measures
论文作者
论文摘要
我们使用单调增加的功能$ f $和Bregman Divergence讨论一类目标函数中的公正估计方程。功能$ f $的选择提供了理想的属性，例如针对异常值的鲁棒性。为了获得公正的估计方程，通常需要在分析上棘手的积分作为偏置校正项。在这项研究中，我们阐明了Bregman差异，统计模型和功能$ F $的组合，其中偏差校正术语消失了。为了关注Mahalanobis和Itakura-saito距离，我们提供了基本现有结果的概括，并用比例参数来表征积极真实的一系列分布，其中包括伽马分布作为一种特殊情况。当异常值的比例很大时，我们讨论了潜在偏置最小化的可能性，这是由偏置校正项的灭绝引起的。
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.
