  The divide and conquer method is a common strategy for handling massive data.
In this article, we study the divide and conquer method for cubic-rate
estimators under the massive data framework. We develop a general theory for
establishing the asymptotic distribution of the aggregated M-estimators using a
simple average. Under certain condition on the growing rate of the number of
subgroups, the resulting aggregated estimators are shown to have faster
convergence rate and asymptotic normal distribution, which are more tractable
in both computation and inference than the original M-estimators based on
pooled data. Our theory applies to a wide class of M-estimators with cube root
convergence rate, including the location estimator, maximum score estimator and
value search estimator. Empirical performance via simulations also validate our
theoretical findings.
