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 local polynomial regression. Using the local 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 is concerned. We express Cook's distance in terms of the local residuals and the local leverages, and express the simplified version of 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 the bandwidth estimator. As an illustrative example, a real data set is analyzed.
