Abstract
Estimating variances and standard errors (SEs) that faithfully reflect all sources of variability in a sample design and an estimator is the goal, but this can be complicated. This is especially true when several (random) weight adjustments are made like nonresponse adjustment and calibration. Several alternative methods of variance estimation that will be covered in this chapter—exact formulas, linearization, and replication variance estimators (jackknife, balanced repeated replication, and bootstrap). We summarize the methods along with some of their strengths and weaknesses, including how easily each can account for different sources of variability. The last two sections of this chapter discuss some specialized topics—combining PSUs or strata for variance estimation and ways of handling certainty PSUs when estimating variances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dippo C. S., Fay R. E., Morganstein D. R. (1984). Computing variances from complex samples with replicate weights. In: Proceedings of the Survey Research Methods Section, American Statistical Association, pp 489–494.
Efron B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. SIAM [Society for Industrial and Applied Mathematics], Philadelphia.
Efron B., Tibshirani R. (1998). An Introduction to the Bootstrap. CRC Press LLC, Boca Raton, FL.
Fay R. E. (1984). Some properties of estimates of variance based on replication methods. In: Proceedings of the Survey Research Methods Section, American Statistical Association, pp 495–500.
Francisco C., Fuller W. A. (1991). Quantile estimation with a complex survey design. Annals of Statistics 19:454–469.
Hansen M. H., Hurwitz W. N., Madow W. G. (1953a). Sample Survey Methods and Theory, Volume I. John Wiley & Sons, Inc., New York.
Judkins D. (1990). Fay’s method of variance estimation. Journal of Official Statistics 6:223–239.
Kang J. D. Y., Schafer J. L. (2007). Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22(4):523–539.
Kott P. S. (1999). Some problems and solutions with a delete-a-group jackknife. In: Federal Committee on Statistical Methodology Research Conference, Vol. 4, U.S. Bureau of the Census, pp 129–135.
Kott P. S. (2001). The delete-a-group jackknife. Journal of Official Statistics 17(4):521–526.
Krewski D., Rao J. N. K. (1981). Inference from stratified samples: Properties of the linearization, jackknife, and balanced repeated replication methods. Annals of Statistics 9:1010–1019.
Lu W., Brick J. M., Sitter R. (2006). Algorithms for constructing combined strata grouped jackknife and balanced repeated replications with domains. Journal of the American Statistical Association 101:1680–1692.
Lumley T. (2010). Complex Surveys. John Wiley & Sons, Inc., New York.
McCarthy P. J. (1969). Pseudo-replication: Half-samples. Review of the International Statistical Institute 37:239–264.
Rao J. N. K., Shao J. (1999). Modified balanced repeated replication for complex survey data. Biometrika 86(2):403–415.
Rao J. N. K., Wu C. F. J. (1985). Inference from stratified samples: Second-order analysis of three methods for nonlinear statistics. Journal of the American Statistical Association 80:620–630.
Rao J. N. K., Wu C. F. J. (1988). Resampling inference with complex survey data. Journal of the American Statistical Association 83:231–241.
RTI International. (2012). SUDAAN Language Manual, Release 11.0. Research Triangle Park, NC.
Rust K. F. (1984). Techniques for estimating variances for sample surveys. PhD thesis, University of Michigan, Ann Arbor MI, unpublished.
Rust K. F. (1985). Variance estimation for complex estimators in sample surveys. Journal of Official Statistics 1:381–397.
Saigo H., Shao J., Sitter R. (2001). A repeated half-sample bootstrap and balanced repeated replications for randomly imputed data. Survey Methodology 27(2):189–196.
Särndal C., Swensson B., Wretman J. (1992). Model Assisted Survey Sampling. Springer, New York.
Shao J., Sitter R. (1996). Bootstrap for imputed survey data. Journal of the American Statistical Association 91:1278–1288.
Sitter R. (1992). Comparing three bootstrap methods for survey data. The Canadian Journal of Statistics/La Revue Canadienne de Statistique 20:135–154.
Valliant R., Dever J. A. (2018). Survey Weights: A Step-by-Step Guide to Calculation. Stata Press, College Station, TX.
Valliant R., Rust K. F. (2010). Degrees of freedom approximations and rules-of-thumb. Journal of Official Statistics 26:585–602.
Valliant R., Dorfman A. H., Royall R. M. (2000). Finite Population Sampling and Inference: A Prediction Approach. John Wiley & Sons, Inc., New York.
Valliant R., Brick J. M., Dever J. A. (2008). Weight adjustments for the grouped jackknife variance estimator. Journal of Official Statistics 24(3):469–488.
Westat. (2007). WesVar 4.3 User’s Guide. Westat, Rockville, MD, URL www.westat.com
Winter N. (2002). svr: Stata SurVey Replication package. URL http://faculty.virginia.edu/nwinter/progs/
Wolter K. M. (2007). Introduction to Variance Estimation, 2nd edn. Springer, New York.
Woodruff R. S. (1952). Confidence intervals for medians and other position measures. Journal of the American Statistical Association 47:635–646.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Valliant, R., Dever, J.A., Kreuter, F. (2018). Variance Estimation. In: Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-93632-1_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-93632-1_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93631-4
Online ISBN: 978-3-319-93632-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)