对~Pareto $\pi$ps 抽样统计性质的研究能够为其在中国农 业抽样调查中应用的可行性提供理论依据.文章对~Pareto $\pi$ps 抽样的~Horvitz-Thompson 估计量方差研究发现: 在大多数实际调查中, 给定抽样比, 总体单元数足够大, ~Pareto $\pi$ps 抽样的~Horvitz-Thompson 估计量方差小于~Poisson 抽样的比估计量方差和~$\pi$ps 系统抽样的~Horvitz-Thompson 估计量方差.选择增长速度慢于目标变量的规模变量有利于增加~Pareto $\pi$ps 抽样~Horvitz-Thompson 估计量方差的相对优势.总体单元数、抽样比的增加、目标变量与规模变量关系调节参数的增大有利于发挥~Pareto $\pi$ps 抽样~Horvitz-Thompson 估计量方差的相对优势.

The statistical property of the Horvitz-Thompson estimator for Pareto $\pi$ps sampling can be provided as a theoretical basis of feasibility in its application of China agricultural sampling survey. This paper gives some properties of the variance of Horvitz-Thompson estimator for Pareto $\pi$ps sampling. In most surveys, when sampling ratio is given and the number of population units is large enough, the variance of the Horvitz-Thompson estimator of Pareto $\pi$ps sampling is smaller than those of the ratio estimator of Poisson sampling, as well of the Horvitz-Thompson estimator of systematic $\pi$ps sampling. For Pareto $\pi$ps sampling, the Horvitz-Thompson estimator has smaller variance when the growth rate of auxiliary variable is slower than the target variable. As the number of population units increases, sampling ratio increases, or the adjusting parameter of the growth rate between the target variable and the auxiliary variable increases, Horvitz-Thompson estimator for Pareto $\pi$ps sampling often has smaller variance.