The strategy of divide-and-combine (DC) has been widely used in the area of big data. Bias-correction is crucial in the DC procedure for validly aggregating the locally biased estimators, especial for the case when the number of batches of data is large. This paper establishes a race-DC through a residual-adjustment composition estimate (race). The race-DC applies to various types of biased estimators, which include but are not limited to Lasso estimator, Ridge estimator and principal component estimator in linear regression, and least squares estimator in nonlinear regression. The resulting global estimator is strictly unbiased under linear model, and is acceleratingly bias-reduced in nonlinear model, and can achieve the theoretical optimality, for the case when the number of batches of data is large. Moreover, the race-DC is computationally simple because it is a least squares estimator in a pro forma linear regression. Detailed simulation studies demonstrate that the resulting global estimator is significantly bias-corrected, and the behavior is comparable with the oracle estimation and is much better than the competitors.
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