Influence diagnostics for ridge regression using the Kullback–Leibler divergence

The identification of anomalous observations provides insight into which aspects of the modeling process may be vulnerable. Thus, appropriate diagnostic measures can be developed to prevent certain types of outlying observations from going undetected. This paper proposes an approach to assess the influence diagnostics in ridge regression based on the Kullback–Leibler divergence. To quantify the impact of observations on the ridge estimator two main procedures are explored. Namely, a case-deletion method and the local influence technique considering several perturbation schemes. We provide tractable expressions to assessing the influence of individual observations as well as the derivatives required to characterize the local curvature. The developed measures correspond to a combination of the leverages and the volume of the confidence ellipsoid, which allows an interesting characterization of the detected observations. To evaluate the performance of the proposed methodology, we consider the analysis of two real datasets and performed a comparison with several methods for outlier detection and assessing influence in ridge regression. In such numerical examples, the proposed measures are successful in identifying observations that are not detected by the traditional techniques.