中文摘要：

多主题抽样调查在实际统计工作中非常普遍,即一项调查同时涉及两个或多个目标变量（指标）,对总体的推算也需要同时对这两个或多个指标进行估计。通常同一调查中的多个目标变量之间会具有相关性,利用这一信息可以提高对所关注调查指标的估计精度。本文利用多重多元线性模型的方法研究这一问题,讨论了最佳线性模型无偏估计和一般回归估计,可以看到借助调查指标之间的相关性,较之常用的单个响应变量的多元线性回归模型方法,得到的最佳线性模型无偏估计和一般回归估计都可以有效地提高对总体总量的估计精度,本文的数值模拟和实例分析也验证了这一结论。

英文摘要：

In the statistical business of sample surveys,there usually cover two or more target variables（ indicators） in one survey program which is a typical multi-purpose survey. When estimating the target variables,we intend to estimate these two or more target variables simultaneously. Usually there are correlations among those surveyed variables,and it could be utilized to improve the estimation for target variables of interest by taking advantage of correlations among surveyed variables. This paper investigates the best linear model-based unbiased estimator and the general regression estimator under the multivariate multiple linear regression model. Compared with the most frequently used model of single response multivariate linear regression,the above two estimators for population total could effectively improve estimation precision. It is also elaborated by the results from the numerical simulation and a real case.