  This paper establishes a global bias-correction divide-and-conquer (GBC-DC)
rule for biased estimation under the case of memory constraint. In order to
introduce the new estimation, a closed representation of the local estimators
obtained by the data in each batch is adopted, aiming to formulate a pro forma
linear regression between the local estimators and the true parameter of
interest. Least square method is then used within this framework to composite a
global estimator of the parameter. Thus, the main advantage over the classical
DC method is that the new GBC-DC method can absorb the information hidden in
the statistical structure and the variables in each batch of data.
Consequently, the resulting global estimator is strictly unbiased even if the
local estimator has a non-negligible bias. Moreover, the global estimator is
consistent, and even can achieve root-$n$ consistency, without the constraint
on the number of batches. Another attractive feature of the new method is
computationally simple and efficient, without use of any iterative algorithm
and local bias-correction. Specifically, the proposed GBC-DC method applies to
various biased estimations such as shrinkage-type estimation and nonparametric
regression estimation. Detailed simulation studies demonstrate that the
proposed GBC-DC approach is significantly bias-corrected, and the behavior is
comparable with the full data estimation and is much better than the
competitors.
