Detecting Multiple Influential Observations in High Dimensional Linear Regression

In this paper, we consider the detection of multiple influential observations in high dimensional regression, where the p number of covariates is much larger than sample size n. Detection of influential observations in high dimensional regression is challenging. In the case of single influential observation, Zhao et al. (2013) developed a method called High dimensional Influence Measure (HIM). However, the result of HIM is not applicable to the case of multiple influential observations, where the detection of influential observations is much more complicated than the case of single influential observation. We propose in this paper a new method based on the multiple deletion to detect the multiple influential.

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