Identifying outliers and influential observations in general linear regression models

Includes bibliographical references (leaves 140-149).Identifying outliers and/or influential observations is a fundamental step in any statistical analysis, since their presence is likely to lead to erroneous results. Numerous measures have been proposed for detecting outliers and assessing the influence of observations on least squares regression results. Since outliers can arise in different ways, the above mentioned measures are based on motivational arguments and they are designed to measure the influence of observations on different aspects of various regression results. In what follows, we investigate how one can combine different test statistics based on residuals and diagnostic plots to identify outliers and influential observations (both in the single and multiple case) in general linear regression models

Localized Regression

The main problem with localized discriminant techniques is the curse of dimensionality, which seems to restrict their use to the case of few variables. This restriction does not hold if localization is combined with a reduction of dimension. In particular it is shown that localization yields powerful classifiers even in higher dimensions if localization is combined with locally adaptive selection of predictors. A robust localized logistic regression (LLR) method is developed for which all tuning parameters are chosen data¡adaptively. In an extended simulation study we evaluate the potential of the proposed procedure for various types of data and compare it to other classification procedures. In addition we demonstrate that automatic choice of localization, predictor selection and penalty parameters based on cross validation is working well. Finally the method is applied to real data sets and its real world performance is compared to alternative procedures