Multivariate Outlier Identification Based on Robust Estimators of Location and Scatter
Real-life data often contain some observations not consistent with the main bulk of the rest. Since classical statistical procedures often react sensitive against so-called outliers, the use of outlier identification methods based on robust statistical estimators is recommended. One class of such robust estimators is constructed according to the principle of subset selection, meaning that an outlier-free subset of the data is identified first which can then be used to discard or downweight deviating observations in order to robustly estimate the parameters of interest. Such approaches also deliver outlier identification methods. The general approach is presented and three methods are discussed which are developed especially for cases where there are no special restrictions on the data structure given by the main bulk of the observations.
- Becker, C., & Paris Scholz, S. (2006). Deepest points and least deep points: robustness and outliers with MZE. In M. Spiliopoulou, R. Kruse, C. Borgelt, A. Nürnberger, & W. Gaul (Eds.), From data and information analysis to knowledge engineering (pp. 254–261). Heidelberg: Springer. CrossRefGoogle Scholar
- Delaunay, B. (1934). Sur la sphere vide. Izvestiâ Akademii Nauk SSSR. Otdelenie Tehničeskih Nauk, 7, 793–800. Google Scholar
- Fieller, N. R. J. (1976). Some problems related to the rejection of outlying observations. Ph.D. Thesis, University of Hull, Hull. Google Scholar
- Kirschstein, T., Liebscher, S., & Becker, C. (2013). Robust estimation of location and scatter by pruning the minimum spanning tree. Submitted for publication. Google Scholar
- Mara, W. (2011). The Chernobyl disaster: legacy and impact on the future of nuclear energy. New York: Marshall Cavendish. Google Scholar
- Murphy, R. B. (1951). On tests for outlying observations. Ph.D. Thesis, Princeton University, Ann Arbor. Google Scholar