加总模型与扩展的高斯-马尔科夫定理

摘要

本文将经典的高斯一马尔科夫定理推广到加总数据层面，探讨三类加总形式下加总模型参数估计的最小方差线性无偏性质；揭示加总模型最小方差线性无偏性与非加总模型最小方差线性无偏性之间的关系。在满足正态误差项的假设下，进一步分析加总模型参数所具有的最优无偏特征。最后运用蒙特卡洛方法对加总模型的参数无偏性特征进行数值模拟。%The paper expands the classical Gauss-Markov theorem into the fields of aggregation model, which focuses on the best linear unbias estimation on the three types of aggregation model and differentiate the best linear unbias estimation between aggregation model and disaggregation model. Furthermore, under the hypothesis on normal distribution, we analyze the best unbias estimation character. At last, we demonstrate the above conclusions with the numerical simulation by the Monte Carlo method.