Abstract

Robust high dimensional estimation is one of the most important problems in statistics. In a high dimensional structure with a small number of non-zero observations, the dimension of the parameters is larger than the sample size. For modeling the sparsity of outlier response vector, we randomly selected a small number of observations and corrupted them arbitrarily. There are two distinct ways to overcome sparsity in the generalized linear model (GLM): in the parameter space, or in the space output. According to several studies in corrupted observation modeling, there is a relationship between robustness and sparsity. In this paper for obtaining robust high dimensional estimation, we proposed a finite mixture of the generalized linear models (FMGLMs). By using simulation with the expectation-maximization (EM) algorithm, we show improved modeling performance.

摘要

稳健的高维估计是统计学中最重要的问题之一。在具有少量非零观测值的高维结构中，参数的维数大于样本量。为了模拟异常值响应向量的稀疏性，我们随机选择少量观察值并任意破坏它们。克服广义线性模型 (GLM) 中的稀疏性有两种不同的方法：在参数空间中，或在空间输出中。根据对损坏的观察建模的几项研究，鲁棒性和稀疏性之间存在关系。在本文中，为了获得稳健的高维估计，我们提出了广义线性模型 (FMGLM) 的有限混合。通过使用期望最大化 (EM) 算法的模拟，