Sequential data weighting procedures for  combined ratio estimators in complex sample surveys

Aylin  Alkaya; H. Öztaş  Ayhan; Alptekin  Esin

doi:https://doi.org/10.59170/stattrans-2017-013

Sequential data weighting procedures for combined ratio estimators in complex sample surveys

Aylin Alkaya Department of Business Administration, Nevşehir Haci Bektaş Veli University, 50300 Nevşehir, Turkey. , H. Öztaş Ayhan Department of Statistics, Middle East Technical University, 06800 Ankara, Turkey. , Alptekin Esin Department of Statistics, Gazi University, 06500 Ankara, Turkey Statistics in Transition new series, vol. 18, 2017, 2, pages: 247-270 Published online: 1 June 2017 https://doi.org/10.59170/stattrans-2017-013

181 Views 11 Downloads

ARTICLE

(English) PDF

ABSTRACT

In sample surveys weighting is applied to data to increase the quality of estimates. Data weighting can be used for several purposes. Sample design weights can be used to adjust the differences in selection probabilities for non-self weighting sample designs. Sample design weights, adjusted for nonresponse and non-coverage through the sequential data weighting process. The unequal selection probability designs represented the complex sampling designs. Among many reasons of weighting, the most important reasons are weighting for unequal probability of selection, compensation for nonresponse, and post-stratification. Many highly efficient estimation methods in survey sampling require strong information about auxiliary variables, x. The most common estimation methods using auxiliary information in estimation stage are regression and ratio estimator. This paper proposes a sequential data weighting procedure for the estimators of combined ratio mean in complex sample surveys and general variance estimation for the population ratio mean. To illustrate the utility of the proposed estimator, Turkish Demographic and Health Survey 2003 real life data is used. It is shown that the use of auxiliary information on weights can considerably improve the efficiency of the estimates

KEYWORDS

combined ratio estimator, data weighting, design weight, nonresponse weighting, Post-stratification, weighting, sequential weighting.

REFERENCES

ARDILLY, P., TILLE, Y., (2006). Sampling methods: exercises and solutions. Translated from French by Leon Jang. Springer Science+Business Media, USA.

AYHAN, H. Ö., (1981). Sources and bias of nonresponse in the Turkish Fertility Survey 1978, Turkish Journal of Population Studies 2–3, pp. 104–148.

AYHAN, H. Ö., (1991). Post–stratification and weighting in sample surveys. Invited paper, Research Symposium '91, State Institute of Statistics, Ankara.

AYHAN, H. Ö., (2003). Combined weighting procedures for post-survey adjustment in complex sample surveys. Bulletin of the International Statistical Institute, 60 (1), pp. 53–54.

BETHLEHEM, J. G., KERSTEN, H. M. P., (1985). On the treatment of nonresponse in sample surveys. Journal of Official Statistics, 1 (3), pp. 287–300.

BETHLEHEM, J. G., KELLER, W. J., (1987). Linear weighting of the sample survey data. Journal of Official Statistics, 3 (2), pp. 141–153.

CASSEL, C. M., SÄRNDAL, C. E., WRETMAN J. H., (1976). Some results on generalized difference estimation and generalized regression estimation for finite populations. Biometrika, 63, pp. 615–620.

CERVANTES, I. F., BRICK, J. F., (2009). Efficacy of Poststratification in Complex Sample Design. Proceedings of the Survey Research Methods Section, American Statistical Association, pp. 4642–4655.

COCHRAN, W. G., (1977). Sampling Techniques. 3rd ed. Wiley, New York.

DEMING, W. E., STEPHAN, F. F., (1940). On a least squares adjustment of a sample frequency table when the expected marginal totals are known. Annals of Mathematical Statistics, 11 (4), pp. 427–444.

DEVILLE, J. C., SARNDAL, C. E., (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87, pp. 376–382.

DEVILLE, J. C., SARNDAL, C. E., SAUTORY, O., (1993). Generalized raking procedure in survey sampling. Journal of the American Statistical Association, 88, pp. 1013–1020.

ESTEVAO, V. M., SÄRNDAL, C. E., (2000). A functional form approach to calibration. Journal of Official Statistics, 16 (4), pp. 379–399.

GUY, P. W., (1979). Small sample theory for poststratification, Doctor of Philosophy, Graduate College of Texas ASM University, Texas.

HAJEK, J., (1971). Comment on a paper of D. Basu, In Foundations of Statistical Inference, Toronto, pp. 236–237.

HOLT, D., ELLIOT, D., (1991). Methods of weighting for unit non-response. The Statistician, 40, pp. 333–342.

HOLT, D., SMITH, T. M. F., (1979). Post stratification. Journal of the Royal Statistical Society, Series A (General), 142 (1), pp. 33–46.

HORVITZ, D. G., THOMPSON, D. J., (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association,47, pp. 663–685.

ISAKI, C. T., FULLER, W. A., (1982). Survey design under the regression superpopulation model. Journal of the American Statistical Association, 77, pp. 89–96.

KALTON, G., CERVANTES, F. I., (2003). Weighting methods. Journal of Official Statistics, 19 (2), pp. 81–97.

KISH, L., (1965). Survey Sampling. John Wiley & Sons, Inc., USA.

KISH, L., (1992). Weighting for unequal Pi. Journal of Official Statistics, 8 (2), pp. 183–200.

KOTT, P. S., (2006). Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32, pp. 133–142.

LITTLE, R. J. A., (1993). Post-stratification: A modeler’s perspective, Journal of The American Statistical Association, 88, pp. 1001–1012.

LITTLE, R. J. A., VARTIVARIAN, S., (2005). Does weighting for nonresponse increase the variance of survey means? Proceedings of American Statistical Association: Section on Survey Research Methods, Minneapolis, pp. 3897–3904.

LU H., GELMAN, A., (2003). A method for estimating design based sampling variances for surveys with weighting, post-stratification, and raking. Journal of Official Statistics, 19(2), pp. 133–151.

OSIER, G., MUSEUX, J. M., (2006). Variance estimation for EU–SILC complex poverty indicators using linearization techniques. European Conference on Quality in Survey Statistics, Luxembourg, pp. 1–11.SÄRNDAL, C. E., (1980). On ? -inverse weighting versus best linear unbiased weighting in probability sampling, Biometrika, 67, pp. 639–650.

SÄRNDAL, C. E., SWENSON, B., WRETMAN, J., (1992). Model assisted survey sampling. Springer–Verlag, New York.

SÄRNDAL, C. E., (2007). The calibration approach in survey theory and practice. Survey Methodology, Statistics Canada, 33 (2), pp. 99–119.

SINGH, S., (2003). Advanced sampling theory with applications. Kluwer Academic Publishers, Dordrecht Boston, London.

SMITH, T. M. F., (1991). Post–stratification. The Statistician, 40, pp. 315–321.

STEPHAN, F. F., (1942). An iterative method of adjusting sample frequency tables when expected marginal totals are known. Annals of Mathematical Statistics, 13 (2), pp. 166–178.

TDHS, (2004). Turkey Demographic and Health Survey 2003. Hacettepe University, Institute of Population Studies, Ankara, Turkey.

TIKKIWAL, G. C., RAI, P. K., GHIYA, A., (2013). On the Performance of Generalized Regression Estimator for Small Domains, Communication in Statistics: Simulation and Computation, 42, pp. 891–909.

VERMA, V., (1991). Sampling Methods. Manual for Statistical Trainers Number 2, Statistical Institute for Asia and the Pacific, Tokyo, Japan.

VERMA, V., (2007). Recent advances in survey sampling. In: Ayhan, H.Ö. and Batmaz, I. (eds.), Recent Advances in Statistics. Turkish Statistical Institute Press, Ankara, Turkey, pp. 77–101.

WRIGHT, R. L., (1983). Finite population sampling with multivariate auxiliary information. Journal of the American Statistical Association, 78, pp. 879–884.

WU, C., SITTER, R. R., (2001). A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96, pp. 185–193.

WU, C., (2003). Optimal calibration estimators in survey sampling. Biometrika, 90(4), pp. 937–951.