Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

The Selection of Strategies for Variance Estimation under πPS Sampling Schemes

  • Published : 2006.04.01
Download PDF
⟨ Previous Next ⟩

Abstract

When using the well-known variance estimator of Sen (1953) and Yates and Grundy (1953) in inclusion probability proportional to size sampling, we often encounter the problems due to the calculation of the joint probabilities. Sarndal (1996) and Knottnerus (2003) proposed alternative strategies for variance estimation to avoid those problems in the traditional method. We discuss some of practical issues that arise when they are used. Also, we describe the traditional strategy using a sampling procedure available in a statistical software. It would be one of the attractive choices for design-based variance estimation.

Keywords

References

  1. Asok, C. and Sukhatme, B.V. (1976). On Sampford's procedure of unequal probability sampling without replacement. Journal of the American Statistical Association, Vol. 71, 912-918 https://doi.org/10.2307/2286860
  2. Bayless, D.L. and Rao, J.N.K. (1970). An empirical study of stabilities of estimators and variance estimators in unequal probability sampling(n = 3 or 4). Journal of the American Statistical Association, Vol. 65, 1645-1667 https://doi.org/10.2307/2284348
  3. Brewer, K.W.R. (1963). A model of systematic sampling with unequal probabilities. Australian Journal of Statistics, Vol. 5, 5-13 https://doi.org/10.1111/j.1467-842X.1963.tb00132.x
  4. Hartley, H.O. and Rao, J.N.K (1962). Sampling with unequal probabilities and without replacement. The Annals of Mathematical Statistics, Vol. 33, 350-374 https://doi.org/10.1214/aoms/1177704564
  5. Cochran, W.G. (1977). Sampling Techniques, John Wiley & Sons, New York
  6. Hidiroglou, M.A., Estevao, V.M., and Arcaro, C. (2000). Generalized estimation system and future enhancements, presented in the International Conference on Establishment Surveys II, Buffalo, New York
  7. Horvitz, D.G. and Thompson, D.J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, Vol. 47, 663-685 https://doi.org/10.2307/2280784
  8. Kish, L. (1995). Survey Sampling, John Wiley & Sons, New York
  9. Knottnerus, P. (2003). Sample Survey Theory, Spring-Verlag, New York
  10. Rao, J.N.K. (1965). On two simple schemes of unequal probability sampling without replacement. Journal of the Indian Statistical Association, Vol. 3, 173-180
  11. Sampford, M.R. (1962). An introduction to sampling theory, Oliver and Boyd, London
  12. Sampford, M.R. (1967). On sampling without replacement with unequal probabilities of selection. Biometrika, Vol. 54, 499-513 https://doi.org/10.1093/biomet/54.3-4.499
  13. Sarndal, C.E. (1996). Efficient estimators with simple variance in unequal probability sampling. Journal of the American Statistical Association, Vol. 91, 1289-1300 https://doi.org/10.2307/2291747
  14. Sarndal, C.E., Swensson, B., and Wretman, J.H. (1992). Model Assisted Survey Sampling, Spring-Verlag, New York
  15. SAS/STAT (2004). User's Guide: The SURVEYSELECT Procedure, Version 9.1, SAS Institute Inc., Cary, NC, USA
  16. SPSS (2004). Base Users Guide: SPSS Complex Samples, Version 13.0, SPSS Inc., Chicago, IL, USA
  17. Sen, A.R. (1953). On the estimate of variance in sampling with varying probabilities. Journal of the Indian Society of Agricultural Statistics, Vol. 5, 119-127
  18. Yates, F. and Grundy, P.M. (1953). Selection without replacement from within strata and with probability proportional to size. Journal of the Royal Statistical Society, Series B, Vol. 15, 253-261