Case influence diagnostics in the lasso regression

Using the diagnostic results in the ridge regression model, we propose an approximate version of Cook’s distance in the lasso regression model since the analytic expression of the lasso estimator is not available. Also, we express the proposed Cook’s distance in terms of basic building blocks such as residuals and leverages. We verify that the proposed statistic successfully detects potentially influential observations on estimators of regression coefficients and on the model selection in the lasso regression model. An illustrative example based on a real dataset is given.