Multivariate functional outlier detection

Functional data are occurring more and more often in practice, and various statistical techniques have been developed to analyze them. In this paper we consider multivariate functional data, where for each curve and each time point a p-dimensional vector of measurements is observed. For functional data the study of outlier detection has started only recently, and was mostly limited to univariate curves (p = 1). In this paper we set up a taxonomy of functional outliers, and construct new numerical and graphical techniques for the detection of outliers in multivariate functional data, with univariate curves included as a special case. Our tools include statistical depth functions and distance measures derived from them. The methods we study are affine invariant in p-dimensional space, and do not assume elliptical or any other symmetry.