Anuradha Roy University of Texas San Antonio: Discriminant Analysis for Multi-level Multivariate Observations
Abstract: Although devised in 1936 by Fisher, discriminant analysis
is still rapidly evolving, as the complexity of contemporary data
sets grows exponentially. Our classification rules explore these
complexities by modeling various correlations in multi-level
multivariate data. Furthermore, our classification rules are suitable
to data sets where the number of response variables is comparable or
larger than the number of observations. We assume that the
multi-level multivariate observations have a doubly exchangeable
covariance structure and different Kronecker product structures on
the mean vectors. The main idea of this talk is to employ the
information of the double exchangeability of a variance-covariance
matrix for three-level data, which allows partitioning a covariance
structure into three unstructured covariance matrices corresponding
to each of the three levels. As a consequence, the number of
estimated covariance parameters is substantially reduced, comparing
to the Fisher's approach, which enables us to apply the proposed
procedures even to a very small number of observations. The new
discriminant functions are very efficient in discriminating
individuals in a small sample scenario. Iterative algorithms are
proposed to calculate the maximum likelihood estimates of the unknown
population parameters as closed form solutions do not exist for these
unknown parameters. The new discriminant functions are applied to a
real data set as well as to simulated data sets. We compare our
findings with the Fisher's discriminant function.
Tillbaka till huvudsidan.