The problem of the estimation of the design-variance and the design-MSE of different estimators and predictors is considered. Bootstrap algorithms applicable to complex sampling designs are used. A generalisation of the bootstrap procedure studied by Quatember (2014) is proposed. In most of the cases considered in our simulation study it leads to more accurate estimates (or to very similar ones in remaining cases) of the design- MSE and the design-variance compared with the original algorithm and its other counteparts.
bootstrap for complex sampling designs, variance estimation, MSE estimation
ANTAL, E., TILLÉ, Y., (2011). A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population, Journal of the American Statistical Association, Vol. 106, No. 494, pp. 534–543.
ANTAL, E., Tillé, Y., (2014). A New Resampling Method for Sampling Designs Without Replacement: The Doubled Half Bootstrap, Computational Statististic, Vol. 29, No. 5, pp. 1345–1363.
BARBIERO, A., MANZI, G., MECATTI, F., (2015). Bootstrapping probabilityproportional- to-size samples via calibrated empirical population, Journal of Statistical Computation and Simulation, Vol. 85, No. 3, pp. 608–620.
BARBIERO, A., MECATTI, F., (2010). Bootstrap algorithms for variance estimation in ?PS sampling, In Complex Data Modeling and Computationally Intensive Statistical Methods edited by P. Mantovan and P. Secchi, pp. 2019–2026. Springer-Verlag, Italia.
BEAUMONT, J. F., PATAK, Z., (2012). On the Generalized Bootstrap for Sample Surveys with Special Attention to Poisson Sampling, International Statistical Review, Vol. 80, No. 1, pp. 127–148.
BREWER, K. E. W., (1975). A simple procedure for sampling ?pswor, Australian & New Zealand Journal of Statistics, Vol. 17, No. 3, pp. 166–172.
BREWER, K. E. W., HANIF M., (1983). Sampling with unequal probabilities, Springer, New York.
DEVILLE, J. C., (1993). Estimation de la variance pour less enquetes en deux phases. Manuscript, INSEE, Paris.
DEVILLE, J. C., SÄRNDAL, C. E., (1992). Calibration estimators in survey sampling, Journal of the American Statistical Association, Vol. 87, pp. 376–382.
EFRON, B., (1979). Bootstrap methods: another look at the jackknife, Annals of Statistics, Vol. 7, pp. 1–26.
HÁJEK, J., (1981). Sampling From a Finite Population, Marcel Dekker, New York.
HOLMBERG, A., (1998). A bootstrap approach to probability proportional to size sampling, Proceedings of Section on Survey Research Methods, American Statistical Association, Washington, pp. 378–383.
HORVITZ, D.G., THOMPSON, D. J., (1952). A Generalization of Sampling Without Replacement From a Finite Universe, Journal of the American Statistical Association, Vol. 47, No. 260, pp. 663–685.
QUATEMBER, A., (2014). The Finite Population Bootstrap – from the Maximum Likelihood to the Horvitz-Thompson Approach, Austrian Journal of Statistics, Vol. 43, pp. 93–102.
R DEVELOPMENT CORE TEAM, (2019). A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna.
RANALLI, M. G., MECATTI, F., (2012). Comparing Recent Approaches for Bootstrapping Sample Survey Data: A First Step Towards a Unified Approach, Proceedings of Section on Survey Research Methods, American Statistical Association, Washington, pp. 4088–4099.
RAO, J. N. K, MOLINA, I., (2015). Small area estimation. Second edition, John Wiley and Sons, Hoboken, New Jersey.
RAO, J. N. K., WU, C. F. J., (1988). Resampling Inference for Complex Survey Data, Journal of American Statistical Association, Vol. 83, pp. 231–241.
ROYALL, R. M., (1976). The Linear Least Squares Prediction Approach to Two-Stage Sampling, Journal of the American Statistical Association, Vol. 71, pp. 657–473.
SÄRNDAL, C. E, (1981). Frameworks for Inference in Survey Sampling with Applications to Small Area Estimation and Adjustment for Nonresponse, Bulletin of the International Statistical Institute, Vol. 49, pp. 494–513.
SÄRNDAL, C. E., SWENSSON, B., WRETMAN, J., (1992). Model Assisted Survey Sampling, Springer-Verlag, New York.
SEN, A. R., (1953). On the estimate of variance in sampling with varying probabilities, Journal of the Indian Society of Agricultural Statistics, Vol. 5, No. 2, pp. 119–127.
SINGH, A. C, MOHL, C. A., (1996). Understanding calibration estimators in survey sampling, Survey Methodology, Vol. 22, pp. 107–115.
SITTER, R. R., (1992). A Resampling Procedure for Complex Survey Data, Journal of the American Statistical Association, Vol. 87, pp. 755–765.
STUKEL, D. M., HIDIROGLOU, M. A., SÄRNDAL, C. E., (1996). Variance estimation for calibration estimators: A comparison of jackknifing versus Taylor linearization, Survey Methodology, Vol. 22, pp. 177–125.
TILLÉ, Y., (2006). Sampling algorithms, Springer-Verlag, New York.
YATES, F., GRUNDY, P. M., (1953). Selection Without Replacement from Within Strata with Probability Proportional to Size, Journal of the Royal Statistical Society, Ser. B, Vol. 15, pp. 235–261.