  Integrating the outputs of multiple classifiers via combiners or
meta-learners has led to substantial improvements in several difficult pattern
recognition problems. In the typical setting investigated till now, each
classifier is trained on data taken or resampled from a common data set, or
(almost) randomly selected subsets thereof, and thus experiences similar
quality of training data. However, in certain situations where data is acquired
and analyzed on-line at several geographically distributed locations, the
quality of data may vary substantially, leading to large discrepancies in
performance of individual classifiers. In this article we introduce and
investigate a family of classifiers based on order statistics, for robust
handling of such cases. Based on a mathematical modeling of how the decision
boundaries are affected by order statistic combiners, we derive expressions for
the reductions in error expected when such combiners are used. We show
analytically that the selection of the median, the maximum and in general, the
$i^{th}$ order statistic improves classification performance. Furthermore, we
introduce the trim and spread combiners, both based on linear combinations of
the ordered classifier outputs, and show that they are quite beneficial in
presence of outliers or uneven classifier performance. Experimental results on
several public domain data sets corroborate these findings.
