Abstract
In previous chapters we considered the variance of estimators in order to determine the sample size and allocation to the design strata. After the sample data are collected, estimates are made and their variances and standard errors (SEs) must be computed. An SE (square root of the estimated variance) is a basic measure of precision that can be used as a descriptive statistic, e.g., as part of a coefficient of variation (CV ), or for making inferences about population parameters via confidence intervals. Estimating SEs that faithfully reflect all sources of (or a significant portion of the) variability in a sample design and an estimator is our goal, but this can be complicated. This is especially true when several (random) weight adjustments described in Chaps 13 and 14 are used. For example, when an adjustment for nonresponse is applied and then weights are raked to population controls, both procedures contribute to the variance of an estimator in addition to the randomness due to selecting the initial sample itself.
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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.H., 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., 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
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Valliant, R., Dever, J.A., Kreuter, F. (2013). Variance Estimation. In: Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6449-5_15
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