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Improved Horvitz-Thompson estimator in survey sampling
Zong, Xianpeng1; Zhu, Rong2; Zou, Guohua1
AbstractThe 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.
KeywordHorvitz-Thompson estimator Inverse probability weighting Hard-threshold Robustness Unequal probability sampling Sampling without/with replacement Ratio estimator
Funding ProjectNational Natural Science Foundation of China[11529101] ; National Natural Science Foundation of China[11331011] ; Ministry of Science and Technology of China[2016YFB0502301]
WOS Research AreaMathematical Methods In Social Sciences ; Mathematics
WOS SubjectSocial Sciences, Mathematical Methods ; Statistics & Probability
WOS IDWOS:000467059100010
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Document Type期刊论文
Corresponding AuthorZhu, Rong
Affiliation1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
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.
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