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Inconsistency Of Resampling Algorithms For High Breakdown Regression Estimators And A New Algorithm, Douglas M. Hawkins, David J. Olive

Articles and Preprints

Since high breakdown estimators are impractical to compute exactly in large samples, approximate algorithms are used. The algorithm generally produces an estimator with a lower consistency rate and breakdown value than the exact theoretical estimator. This discrepancy grows with the sample size, with the implication that huge computations are needed for good approximations in large high-dimensioned samples

The workhorse for HBE has been the ‘elemental set’, or ‘basic resampling’ algorithm. This turns out to be completely ineffective in high dimensions with high levels of contamination. However, enriching it with a “concentration” step turns it into a method that is able …

Applications Of Robust Distances For Regression, David J. Olive

Articles and Preprints

The DD plot, introduced by Rousseeuw and Van Driessen (1999), is a plot of classical vs robust Mahalanobis distances: MD_i vs RD_i. The DD plot can be used as a diagnostic for multivariate normality and elliptical symmetry, and to assess the success of numerical transformations towards elliptical symmetry. In the regression context, many procedures can be adversely affected if strong nonlinearities are present in the predictors. Even if strong nonlinearities are present, the robust distances can be used to help visualize important regression models such as generalized linear models.

Orthogonal Arrays Of Strength Three From Regular 3-Wise Balanced Designs, Charles J. Colbourn, D. L. Kreher, John P. Mcsorley, D. R. Stinson

Articles and Preprints

The construction given in Kreher, J Combin Des 4 (1996) 67 is extended to obtain new infinite families of orthogonal arrays of strength 3. Regular 3-wise balanced designs play a central role in this construction.