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The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment

Author

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  • Lorenzo Fattorini

    (University of Siena)

  • Timothy G. Gregoire

    (Yale University)

  • Sara Trentini

    (University of Siena)

Abstract

The purpose of this note is to propose a variance estimator under non-measurable designs that exploits the existence of an auxiliary variable well correlated with the survey variable of interest. Under non-measurable designs, the Sen–Yates–Grundy variance estimator generates a downward bias that can be reduced using a calibration weighting based on the auxiliary variable. Conditions of approximate unbiasedness for the resulting calibration estimator are given. The application to systematic sampling is considered. The proposal proves to be effective for estimating the variance of the forest cover estimator in remote sensing-based surveys, owing to the strong correlation between the reference data, available from a systematic sample, and the satellite map data, available for the whole population and hence exploited as an auxiliary variable. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Lorenzo Fattorini & Timothy G. Gregoire & Sara Trentini, 2018. "The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(3), pages 358-373, September.
    • Handle: RePEc:spr:jagbes:v:23:y:2018:i:3:d:10.1007_s13253-018-0325-x
    DOI: 10.1007/s13253-018-0325-x
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    References listed on IDEAS

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    1. Jean D. Opsomer & Mario Francisco-Fernández & Xiaoxi Li, 2012. "Model-Based Non-parametric Variance Estimation for Systematic Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 528-542, September.
    2. Anton Grafström & Niklas L. P. Lundström & Lina Schelin, 2012. "Spatially Balanced Sampling through the Pivotal Method," Biometrics, The International Biometric Society, vol. 68(2), pages 514-520, June.
    3. Stevens, Don L. & Olsen, Anthony R., 2004. "Spatially Balanced Sampling of Natural Resources," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 262-278, January.
    4. Lorenzo Fattorini, 2006. "Applying the Horvitz-Thompson criterion in complex designs: A computer-intensive perspective for estimating inclusion probabilities," Biometrika, Biometrika Trust, vol. 93(2), pages 269-278, June.
    5. Giorgio Montanari & Francesco Bartolucci, 1998. "On estimating the variance of the systematic sample mean," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(2), pages 185-196, August.
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    Cited by:

    1. Maria Michela Dickson & Giuseppe Espa & Lorenzo Fattorini & Flavio Santi, 2022. "Double-calibration estimators accounting for under-coverage and nonresponse in socio-economic surveys," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1273-1288, December.
    2. Cindy L. Yu & Jie Li & Michael G. Karl & Todd J. Krueger, 2020. "Obtaining a Balanced Area Sample for the Bureau of Land Management Rangeland Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 250-275, June.

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