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Forward search outlier detection in data envelopment analysis. (English) Zbl 1237.90107

Summary: We tackle the problem of outlier detection in data envelopment analysis (DEA). We propose a procedure where we merge the super-efficiency DEA and the forward search. Since DEA provides efficiency scores which are not parameters to fit the model to the data, we introduce a distance, to be monitored along the search. This distance is obtained through the integration of a regression model and the super-efficiency DEA. We simulate a Cobb – Douglas production function and we compare the super-efficiency DEA and the forward search analysis in both uncontaminated and contaminated settings. For inference about outliers, we exploit envelopes obtained through Monte Carlo simulations.

MSC:

90B50 Management decision making, including multiple objectives
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
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[1] Atkinson, A.C.; Riani, M., Robust diagnostic regression analysis, (2000), Springer-Verlag New York · Zbl 0964.62063
[2] Atkinson, A.C.; Riani, M.; Cerioli, A., Exploring multivariate data with the forward search, (2004), Springer-Verlag New York · Zbl 1049.62057
[3] Banker, R.D.; Gifford, J.L., A relative efficiency model for the evaluation of public health nurse productivity, (1988), Carnegie Mellon University Mimeo Pittsburg, PA, USA
[4] Banker, R.D.; Chang, H., The super-efficiency procedure for outlier identification, not for ranking efficient units, European journal of operational research, 175, 1311-1320, (2006) · Zbl 1142.90417
[5] Banker, R.D.; Charnes, A.; Cooper, W.W., Some models for estimating technical and scale efficiencies in data envelopment analysis, Management science, 30, 1078-1092, (1984) · Zbl 0552.90055
[6] Bellini, T., Detecting atypical observations in financial data: the forward search for elliptical copulas, Advances in data analysis and classification, 4, 287-299, (2010) · Zbl 1284.62194
[7] Bellini, T., Riani, M., 2011. Robust analysis of default intensity. Computational Statistics and Data Analysis, in press. doi:10.1016/j.csda.2011.03.007. · Zbl 1254.91635
[8] Charnes, A.; Cooper, W.W.; Rhodes, E., Measuring the efficiency of decision making units, European journal of operational research, 2, 429-444, (1978) · Zbl 0416.90080
[9] Kuosmanen, T.; Johnson, A.L., Data envelopment analysis as nonparametric least squares regression, Operations research, 58, 1, 149-160, (2010) · Zbl 1233.90220
[10] Lovell, C.A.K.; Rouse, A.P.B., Equivalent standard DEA models to provide super-efficiency scores, Journal of the operational research society, 54, 101-108, (2003) · Zbl 1088.90519
[11] Riani, M.; Zani, S., An iterative method for the detection of multivariate outliers, Metron, 55, 101-117, (1997) · Zbl 0938.62067
[12] Zani, S.; Riani, M.; Corbellini, A., Robust bivariate boxplots and multiple outlier detection, Computational statistics and data analysis, 24, 257-270, (1998) · Zbl 1042.62545
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