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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.

A robust high dimensional estimation of a finite mixture of the generalized linear model