  In modern scientific research, massive datasets with huge numbers of
observations are frequently encountered. To facilitate the computational
process, a divide-and-conquer scheme is often used for the analysis of big
data. In such a strategy, a full dataset is first split into several manageable
segments; the final output is then averaged from the individual outputs of the
segments. Despite its popularity in practice, it remains largely unknown that
whether such a distributive strategy provides valid theoretical inferences to
the original data. In this paper, we address this fundamental issue for the
distributed kernel regression (DKR), where the algorithmic feasibility is
measured by the generalization performance of the resulting estimator. To
justify DKR, a uniform convergence rate is needed for bounding the
generalization error over the individual outputs, which brings new and
challenging issues in the big data setup. Under mild conditions, we show that,
with a proper number of segments, DKR leads to an estimator that is
generalization consistent to the unknown regression function. The obtained
results justify the method of DKR and shed light on the feasibility of using
other distributed algorithms for processing big data. The promising preference
of the method is supported by both simulation and real data examples.
