Visualizing Influential Observations in Dependent Data

Abstract

We introduce the hair-plot to visualize influential observations in dependent data. It consists of all trajectories of the value of an estimator when each observation is modified in turn by an additive perturbation. We define two measures of influence: the local influence which describes the rate of departure from the original estimate due to a small perturbation of each observation; and the asymptotic influence which indicates the influence on the original estimate of the most extreme contamination for each observation. The cases of estimators defined as quadratic forms or ratios of quadratic forms are investigated in detail. Sample autocovariances, covariograms, and variograms belong to the first case. Sample autocorrelations, correlograms, and indices of spatial autocorrelation such as Moran’s I belong to the second case. We illustrate our approach on various datasets from time series analysis and spatial statistics. This article has supplementary material online.