Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions
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abstract
Mixtures of multivariate contaminated shifted asymmetric Laplace
distributions are developed for handling asymmetric clusters in the presence of
outliers (also referred to as bad points herein). In addition to the parameters
of the related non-contaminated mixture, for each (asymmetric) cluster, our
model has one parameter controlling the proportion of outliers and one
specifying the degree of contamination. Crucially, these parameters do not have
to be specified a priori, adding a flexibility to our approach that is absent
from other approaches such as trimming. Moreover, each observation is given a
posterior probability of belonging to a particular cluster, and of being an
outlier or not; advantageously, this allows for the automatic detection of
outliers. An expectation-conditional maximization algorithm is outlined for
parameter estimation and various implementation issues are discussed. The
behaviour of the proposed model is investigated, and compared with
well-established finite mixtures, on artificial and real data.
