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UBC Theses and Dissertations

The detection and testing of multivariate outliers White, Richard Alan


The classical estimators of multivariate location and scatter for the normal model are the sample mean and sample covariance. However, if outliers are present in the data, the classical estimates can be very inaccurate and robust estimates should be used in their place. Most multivariate robust estimators are very difficult if not impossible to compute, thus limiting their use. I will present some simple approximations that make these estimators computable. Robust estimation down weighs or completely ignores the outliers. This is not always best because the outliers can contain some very important information about the population. If they can be identified, the outliers can be further investigated and an appropriate action can be taken based on the results. To detect outliers, a sequential multivariate scale-ratio test is proposed. It is based on a non-robust estimate and a robust estimate of scatter and is applied in a forward fashion, removing the most extreme point at each step, until the test fails to indicate the presence of outliers. We will show that this procedure has level c when applied to an uncontaminated sample, is uneffected by swamping or masking and is accurate in detecting outliers. Finally, we will apply the scale-ratio test to several data sets and compare it to the sequential Wilk’s outlier test as proposed by C. Caroni and P. Prescott in 1992.

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