  We develop a novel approach to explain why AdaBoost is a successful
classifier. By introducing a measure of the influence of the noise points (ION)
in the training data for the binary classification problem, we prove that there
is a strong connection between the ION and the test error. We further identify
that the ION of AdaBoost decreases as the iteration number or the complexity of
the base learners increases. We confirm that it is impossible to obtain a
consistent classifier without deep trees as the base learners of AdaBoost in
some complicated situations. We apply AdaBoost in portfolio management via
empirical studies in the Chinese market, which corroborates our theoretical
propositions.
