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### Pareto $\pi$ps 抽样的~Horvitz-Thompson 估计量方差研究

1. 天津财经大学统计学院和中国经济统计研究中心, 天津 300222
• 出版日期:2018-04-25 发布日期:2021-06-29

YANG Guijun, WU Jieqiong. On the Variance of the Horvitz-Thompson Estimator for Pareto $\pi$ps Sampling[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 1150-1163.

### On the Variance of the Horvitz-Thompson Estimator for Pareto $\pi$ps Sampling

YANG Guijun, WU Jieqiong

1. School of Statistics and China Center of Economic Statistics Research, Tianjin University of Finance and Economics, Tianjin 300222
• Online:2018-04-25 Published:2021-06-29

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.
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