中文摘要：

一元抽样调查的理论已经发展相对成熟．但实际问题中往往涉及多个指标，一元理论不能满足需要．本文研究了多元二相抽样，并且在多元二相抽样中添加了一元辅助信息。定义了采用一元辅助信息的多元比估计，得到了采用一元辅助信息的多元二相抽样的比估汁量及其性质．并且证明了在满足一定条件时．采用一元辅助信息的多元二相抽样的比估计量优于多元简单随机抽样的简单估计量．

英文摘要：

Presently, the single sampling survey has already usually too many indexes are involved which makes it difficult for come to maturity, but, in practice, the survey to deal with. To meet need of survey, multivariate two-phase sampling complemented with single auxiliary informatio developed. The multivariate ratio estimation with use of single auxiliary information is defined and estimator is attained two-phase sampling It is proved that under complemented with sin the n is specific conditions, the ratio estimator of multivariate gle auxiliary information is better than the simple estimator of multivariate simple random sampling.