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ERIC Number: ED425176
Record Type: Non-Journal
Publication Date: 1998-May
Pages: 7
Abstractor: N/A
Reference Count: N/A
Robust Means and Covariance Matrices by the Minimum Volume Ellipsoid (MVE).
Blankmeyer, Eric
P. Rousseeuw and A. Leroy (1987) proposed a very robust alternative to classical estimates of mean vectors and covariance matrices, the Minimum Volume Ellipsoid (MVE). This paper describes the MVE technique and presents a BASIC program to implement it. The MVE is a "high breakdown" estimator, one that can cope with samples in which as many as half the observations are contaminated. Samples from a multivariate normal distribution form ellipsoid-shaped "clouds" of data points. The MVE corresponds to the smallest such point cloud containing at least half of the observations, the uncontaminated portion of the data. These "clean" observations are used for preliminary estimates of the mean vector and the covariance matrix. Using these estimates, the program next computes a robust Mahalanobis distance for every observation vector in the sample. Observations for which the robust Mahalanobis distances exceed the 97.5% significance level for the chi-square distribution are flagged as probable outliers. Applications of the MVE are outlined, and a BASIC program is provided so that users can try the algorithm on small or medium data sets before obtaining a more comprehensive version. (SLD)
Publication Type: Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A