  The issues of bias-correction and robustness are crucial in the strategy of
divide-and-conquer (DC), especially for asymmetric nonparametric models with
massive data. It is known that quantile-based methods can achieve the
robustness, but the quantile estimation for nonparametric regression has
non-ignorable bias when the error distribution is asymmetric. This paper
explores a global bias-corrected DC by quantile-matched composite for
nonparametric regressions with general error distributions. The proposed
strategies can achieve the bias-correction and robustness, simultaneously.
Unlike common DC quantile estimations that use an identical quantile level to
construct a local estimator by each local machine, in the new methodologies,
the local estimators are obtained at various quantile levels for different data
batches, and then the global estimator is elaborately constructed as a weighted
sum of the local estimators. In the weighted sum, the weights and quantile
levels are well-matched such that the bias of the global estimator is corrected
significantly, especially for the case where the error distribution is
asymmetric. Based on the asymptotic properties of the global estimator, the
optimal weights are attained, and the corresponding algorithms are then
suggested. The behaviors of the new methods are further illustrated by various
numerical examples from simulation experiments and real data analyses. Compared
with the competitors, the new methods have the favorable features of estimation
accuracy, robustness, applicability and computational efficiency.
