A multivariate adaptive trimmed likelihood algorithm

Schubert, Daniel (2005) A multivariate adaptive trimmed likelihood algorithm. PhD thesis, Murdoch University.

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Abstract

The research reported in this thesis describes a new algorithm which can be used to robustify statistical estimates adaptively. The algorithm does not require any pre-specified cut-off value between inlying and outlying regions and there is no presumption of any cluster configuration. This new algorithm adapts to any particular sample and may advise the trimming of a certain proportion of data considered extraneous or may divulge the structure of a multi-modal data set. Its adaptive quality also allows for the confirmation that uni-modal, multivariate normal data sets are outlier free. It is also shown to behave independently of the type of outlier, for example, whether applied to a data set with a solitary observation located in some extreme region or to a data set composed of clusters of outlying data, this algorithm performs with a high probability of success.