The thesis studies robust methods for estimating location and scatter of multivariate distributions and contributes to the development of some aspects regarding the detection of multiple outliers. A variety of methods have been designed for detecting single point outliers which, when applied to groups of contaminated data, lead to problems of "masking", that is when an outlier appears as a "good" data. Robust high-breakdown estimators overcome the masking effect, also allowing for a high tolerance of "bad" data. The Minimum Volume Ellipsoid (MVE) and the Minimum Covariance Determinant estimator (MCD) are the most widely used high-breakdown estimators. The central problem when identifying an anomaly is setting a decision rule. The exact distribution of the MCD and MVE is not known, implying that the diagnostics constructed as a function of these robust estimates have also an unknown distribution. Single point oultiers can be recognized using Mahalanobis distances; multivariate outliers are detected by robust (via MCD and MVE) distances of Mahalanobis type. The thesis obtains the small sample distribution of the first ones in an alternative simpler way than the proof existing in the literature. Furthermore, some empirical evidences show the need of a correction factor to improve the approximation to the expected distribution. Some graphical devices are suggested to enhance the results. One of the limiting aspects of the literature on robustness is the lack of real data applications beside the literature examples. The personal interest in financial subjects has driven the thesis to consider applications in this area. Particular attention is paid to methods for optimal selection of financial portfolios. Mean-Variance portfolio theory selects the assets which maximize the return and minimize the risk of the investment using Maximum Likelihood Estimates (MLE). However, MLE are known to be sensitive to relatively small fractions of outliers. Furthermore, a wide financial literature provides evidence of the non-gaussian distribution of the stock returns. All these reasons motivate the construction of a robust portfolio selection model proposed in the thesis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:645589 |
| Date | January 2004 |
| Creators | Costanzo, Simona |
| Publisher | London School of Economics and Political Science (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.lse.ac.uk/2298/ |
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