基于矩方法的参数的分布式估计框架  

Distributed Parameter Estimation Framework Based on Moment Method

作　　者：宁晓艳 夏志明 NING XIAOYAN;XIA ZHIMING(School of Mathematics,Northwest University,Xi'an 710127,China)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《应用数学学报》2024年第4期656-671,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11771353)资助项目。

摘　　要：在大数据环境下,由于计算机的存储,计算能力和安全隐私等问题,传统的集中式方法不再可行,因此本文基于矩的分布式估计构造了一般参数的分布式估计框架.首先将待估参数表示为多个矩的函数形式,其次对每个矩参数通过简单平均的分布式框架获得其无偏估计,最后将矩参数的分布式无偏估计带入聚合函数得到待估参数的最终估计量.从理论上证明了在一般的条件下,本文估计量的概率收敛界与集中式估计同阶并且具有渐近正态性.模拟实验验证了本文估计量与集中式估计量具有相近的统计性质,同时表现出更优异的计算效率.In the big data environment,the traditional centralized method is no longer feasible due to the problems of computer storage,computing power,security and privacy.In the context of massive data sets,due to the limitations of data collection,transmission and management,complete data sets are usually difficult to obtain.Statistical inference must rely on the inference results of local data sets to reduce the important problems in the research of estimation bias based massive data regression methods.Therefore,this paper constructs a distributed estimation framework for general parameters based on moment distributed estimation,which improves the computing and storage capabilities and solves the problem of depolarization in distributed environments.Firstly,the parameter to be estimated is expressed as a function of multiple moments.Secondly,the unbiased estimation of each moment parameter is obtained through a simple average distributed framework.Finally,the distributed unbiased estimation of the moment parameter is brought into the aggregate function to obtain the final estimator of the parameter to be estimated The theoretical results show that under general conditions,the probability convergence bound of the estimator is the same order as the centralized estimator and the estimator has asymptotic normality The simulation results show that the distributed estimator and the centralized estimator have similar statistical efficiency and better computational efficiency.

关 键 词：分布式 矩方法 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]