论文标题
统一的健壮估计
Unified Robust Estimation
论文作者
论文摘要
强大的估计主要与在存在异常值的存在下提供可靠的参数估计值有关。在回归和分类中提出了许多强大的损失函数以及各种计算算法。但是，在现代惩罚的广义线性模型（GLM）中，对健壮估计的研究有限，可以提供权重确定观测值的异常情况。本文提出了一个基于巨大损失函数的统一框架，这是凹形和凸功能的综合框架（CC家庭）。研究了CC家庭的性质，并通过迭代重新加权的凸优化（IRCO）进行了创新的CC估计，这是对稳定线性回归中迭代重新加权最小二乘的概括。对于健壮的GLM，IRCO成为迭代重新持续的GLM。统一的框架包含惩罚估计和强大的支持向量机，并通过多种数据应用进行了证明。
Robust estimation is primarily concerned with providing reliable parameter estimates in the presence of outliers. Numerous robust loss functions have been proposed in regression and classification, along with various computing algorithms. In modern penalised generalised linear models (GLM), however, there is limited research on robust estimation that can provide weights to determine the outlier status of the observations. This article proposes a unified framework based on a large family of loss functions, a composite of concave and convex functions (CC-family). Properties of the CC-family are investigated, and CC-estimation is innovatively conducted via the iteratively reweighted convex optimisation (IRCO), which is a generalisation of the iteratively reweighted least squares in robust linear regression. For robust GLM, the IRCO becomes the iteratively reweighted GLM. The unified framework contains penalised estimation and robust support vector machine and is demonstrated with a variety of data applications.
