Improved Horvitz-Thompson estimator in survey sampling

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	Improved Horvitz-Thompson estimator in survey sampling
	Zong, Xianpeng 1; Zhu, Rong2 ; Zou, Guohua 1
	2019
发表期刊	SURVEY METHODOLOGY
ISSN	0714-0045
卷号	45 期号:1 页码:165-184
摘要	The Horvitz-Thompson (HT) estimator is widely used in survey sampling. However, the variance of the HT estimator becomes large when the inclusion probabilities are highly heterogeneous. To overcome this shortcoming, in this paper we propose a hard-threshold method for the first-order inclusion probabilities. Specifically, we carefully choose a threshold value, then replace the inclusion probabilities smaller than the threshold by the threshold. Through this shrinkage strategy, we construct a new estimator called the improved Horvitz-Thompson (IHT) estimator to estimate the population total. The IHT estimator increases the estimation accuracy much although it brings a bias which is relatively small. We derive the IHT estimator's mean squared error and its unbiased estimator, and theoretically compare the IHT estimator with the HT estimator. We also apply our idea to construct an improved ratio estimator. We numerically analyze simulated and real data sets to illustrate that the proposed estimators are more efficient and robust than the classical estimators.
关键词	Horvitz-Thompson estimator Inverse probability weighting Hard-threshold Robustness Unequal probability sampling Sampling without/with replacement Ratio estimator
语种	英语
资助项目	National Natural Science Foundation of China[11529101] ; National Natural Science Foundation of China[11331011] ; Ministry of Science and Technology of China[2016YFB0502301]
WOS研究方向	Mathematical Methods In Social Sciences ; Mathematics
WOS类目	Social Sciences, Mathematical Methods ; Statistics & Probability
WOS记录号	WOS:000467059100010
出版者	STATISTICS CANADA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34680
专题	系统科学研究所
通讯作者	Zhu, Rong
作者单位	1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zong, Xianpeng,Zhu, Rong,Zou, Guohua. Improved Horvitz-Thompson estimator in survey sampling[J]. SURVEY METHODOLOGY,2019,45(1):165-184.
APA	Zong, Xianpeng,Zhu, Rong,&Zou, Guohua.(2019).Improved Horvitz-Thompson estimator in survey sampling.SURVEY METHODOLOGY,45(1),165-184.
MLA	Zong, Xianpeng,et al."Improved Horvitz-Thompson estimator in survey sampling".SURVEY METHODOLOGY 45.1(2019):165-184.