A predictive DEA model for outlier detection

Outlier detection is one of the key issues in any data-driven analytics.In this paper,we propose Bi-super DEA,a super DEA-based method that constructs both efficient and inefficient frontiers for outlier detection.In evaluating its predictive performance,we develop a novel predictive DEA procedure,PDEA,which extends the conventional DEA approaches that have been primarily used for in-sample efficiency estimation,to predict outputs for the out-of-sample.This enables us to compare the predictive performance of our approach against several popular outlier detection methods including the parametric robust regression in statistics and non-parametric k-means in data mining.We conduct comprehensive simulation experiments to examine the relative performance of these outlier detection methods under the influence of five factors:sample size,linearity of production function,normality of noise distribution,homogeneity of data,and levels of random noise contaminating the data generating process(DGP).We find that,somewhat surprisingly,Bi-super CCR consistently outperforms Bi-super BCC in detecting outliers.Under the linearity,normality and homogeneity conditions,the parametric robust regression method works best.However,when the DGP violates these conditions,Bi-super DEA emerges as the better choice due to its distribution-free property.Our results shed light on the conditions that each method excels or fails and provide users with practical guidelines on how to choose appropriate methods to detect outliers.