论文标题
在异质性下加权分布式估计
Weighted Distributed Estimation under Heterogeneity
论文作者
论文摘要
本文考虑在分布式数据块之间在异质分布下考虑分布的M估计。提出了加权分布式估计器，以提高所有数据块共享的公共参数的标准“拆分和扭曲）估计器的效率。加权分布式估计器至少与可能的完整样本和矩估计器的广义方法一样高，后两个估计器需要完整的数据访问。与现有方法相比，WD估算器的偏差减少是为了适应大量的数据块，而无需牺牲估计效率，并且对SAC估计器进行了类似的证明操作。均方根误差（MSE）界限以及WD的渐近分布和两个证明估计量的范围被得出，当数据块的数量较大时，该估计量显示出偏差的估计量的有利性能。
This paper considers distributed M-estimation under heterogeneous distributions among distributed data blocks. A weighted distributed estimator is proposed to improve the efficiency of the standard "Split-And-Conquer" (SaC) estimator for the common parameter shared by all the data blocks. The weighted distributed estimator is shown to be at least as efficient as the would-be full sample and the generalized method of moment estimators with the latter two estimators requiring full data access. A bias reduction is formulated to the WD estimator to accommodate much larger numbers of data blocks than the existing methods without sacrificing the estimation efficiency, and a similar debiased operation is made to the SaC estimator. The mean squared error (MSE) bounds and the asymptotic distributions of the WD and the two debiased estimators are derived, which shows advantageous performance of the debiased estimators when the number of data blocks is large.
