Identification of Influential Observations for High-Dimensional Regression

The prevalence of high-dimensional datasets has driven increased utilization of the penalized likelihood methods. However, when the number of observations is relatively few compared to the number of covariates, each observation can tremendously influence model selection and inference. Therefore, identifying and assessing influential observations is vital in penalized methods. This article reviews measures of influence for detecting influential observations in high-dimensional lasso regression and has recently been introduced. Then, these measures under the elastic net method, which combines removing from lasso and reducing the ridge coefficients to improve the model predictions, are investigated. Through simulation and real datasets, illustrate that introduced influence measures effectively identify influential observations and can help reveal otherwise hidden relationships in the data.