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Variable Selection For 1d Regression Models, David J. Olive, Douglas M. Hawkins
Variable Selection For 1d Regression Models, David J. Olive, Douglas M. Hawkins
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Variable selection, the search for j relevant predictor variables from a group of p candidates, is a standard problem in regression analysis. The class of 1D regression models is a broad class that includes generalized linear models. We show that existing variable selection algorithms, originally meant for multiple linear regression and based on ordinary least squares and Mallows’ Cp, can also be used for 1D models. Graphical aids for variable selection are also provided.
Two Simple Resistant Regression Estimators, David J. Olive
Two Simple Resistant Regression Estimators, David J. Olive
Articles and Preprints
Two simple resistant regression estimators with OP(n−1/2) convergence rate are presented. Ellipsoidal trimming can be used to trim the cases corresponding to predictor variables x with large Mahalanobis distances, and the forward response plot of the residuals versus the fitted values can be used to detect outliers. The first estimator uses ten forward response plots corresponding to ten different trimming proportions, and the final estimator corresponds to the “best” forward response plot. The second estimator is similar to the elemental resampling algorithm, but sets of O(n) cases are used instead of randomly …