Spatially Smoothed Robust Covariance Estimation for Local Outlier Detection

Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real datasets from various application areas. This article introduces a new outlier detection method that accounts for a (continuously) varying covariance structure, depending on the spatial neighborhood of the observations. The underlying estimator thus constitutes a compromise between a unified global covariance estimation, and local covariances estimated for individual neighborhoods. Theoretical properties of the estimator are presented, in particular related to robustness properties, and an efficient algorithm for its computation is introduced. The performance of the method is evaluated and compared based on simulated data and for a dataset recorded from Austrian weather stations. Supplemental materials to the article are available online.