Robust Means and Covariance Matrices by the Minimum Volume Ellipsoid (MVE).

Autor/in	Blankmeyer, Eric
Titel	Robust Means and Covariance Matrices by the Minimum Volume Ellipsoid (MVE).
Quelle	(1998), (7 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
Schlagwörter	Algorithms; Chi Square; Estimation (Mathematics); Robustness (Statistics); Sample Size + Suchen Sie Ihr Suchwort? Algorithm; Algorithmus; Estimation; Mathematics; Schätzung; Widerstandsfähigkeit
Abstract	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)
Erfasst von	ERIC (Education Resources Information Center), Washington, DC