Survey Methodology
Improved Horvitz-Thompson estimator in survey sampling

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by Xianpeng Zong, Rong Zhu and Guohua ZouNote 1

  • Release date: May 7, 2019
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Abstract

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.

Key Words:      Horvitz-Thompson estimator; Inverse probability weighting; Hard-threshold; Robustness; Unequal probability sampling; Sampling without/with replacement; Ratio estimator.

Table of contents

How to cite

Zong, X., Zhu, R. and Zou, G. (2019). Improved Horvitz-Thompson estimator in survey sampling. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 45, No. 1. Paper available at https://www150.statcan.gc.ca/n1/pub/12-001-x/2019001/article/00007-eng.htm.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in survey methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2019

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. HT estimator and its drawback
Section 3. Improved HT estimator
Section 4. Extension to the ratio estimator
Section 5. Numerical studies
Section 6. Concluding remarks
Acknowledgements
Appendix
References

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