  The principal support vector machines method (Li et al., 2011) is a powerful
tool for sufficient dimension reduction that replaces original predictors with
their low-dimensional linear combinations without loss of information. However,
the computational burden of the principal support vector machines method
constrains its use for massive data. To address this issue, we in this paper
propose two distributed estimation algorithms for fast implementation when the
sample size is large. Both the two distributed sufficient dimension reduction
estimators enjoy the same statistical efficiency as merging all the data
together, which provides rigorous statistical guarantees for their application
to large scale datasets. The two distributed algorithms are further adapt to
principal weighted support vector machines (Shin et al., 2016) for sufficient
dimension reduction in binary classification. The statistical accuracy and
computational complexity of our proposed methods are examined through
comprehensive simulation studies and a real data application with more than
600000 samples.
