Yong Min Im
ABSTRACT
When estimate statistically some parameters using some samples which have various contamination characters, finite sample breakdown point of the estimator is an important criterion for judging if the estimator is useful or not. In most cases, finite sample breakdown point of the robust estimators introduced in the literature was evaluated when samples were in the general case. We propose newly a degree of deviation of samples from the general case as an extension factor of extended general case and establish its effect on existence and finite sample breakdown point of minimum volume ellipsoid estimator of multivariate location and scatter. The larger deviation from the general position of samples where the extension factor is 1 yields the larger extension factor. Finite sample breakdown point of the estimators based on the samples with larger deviation from the general position of samples is smaller than that of the general position of samples and thus the estimators of the case where an extension factor is too large is broken.
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Index Terms
- Finite Sample Breakdown Point of the Minimum Volume Ellipsoid Estimator in Extended General Position of Sample
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