  Margin-based classifiers have been popular in both machine learning and
statistics for classification problems. Since a large number of classifiers are
available, one natural question is which type of classifiers should be used
given a particular classification task. We answer this question by
investigating the asymptotic performance of a family of large-margin
classifiers under the two component mixture models in situations where the data
dimension $p$ and the sample $n$ are both large. This family covers a broad
range of classifiers including support vector machine, distance weighted
discrimination, penalized logistic regression, and large-margin unified machine
as special cases. The asymptotic results are described by a set of nonlinear
equations and we observe a close match of them with Monte Carlo simulation on
finite data samples. Our analytical studies shed new light on how to select the
best classifier among various classification methods as well as on how to
choose the optimal tuning parameters for a given method.
