Cook's Distance in P-Spline Regression

In fitting parametric or nonparametric regression models, one or a few observations may have undue effects on estimators. These influential observations are precisely detected by the well-known influence measure, Cook's distance. In this paper, we introduce a type of Cook's distance for one or a set of observations in logistic P-spline regression. Using the B-spline property we simplify the Cook's distance in a numerical sense. In fact, it turned out that the simplified Cook's distance behaves quite well as far as detecting influential observations are concerned. We express Cook's distance in terms of the ordinary residuals and leverages. We suggest a way of obtaining reference values for Cook's distances. We also consider influential observations on Generalized Cross Validation. As an illustrative example, a real data set is analyzed