Sampling design variance estimation of small area estimators in the Spanish Labour Force survey

  1. Herrador Cansado, Montserrat
  2. Morales González, Domingo
  3. Esteban Álvarez, María Dolores
  4. Sánchez, Ángel
  5. Santamaría Arana, Laureano
  6. Pérez Mas, Antonio
  7. Marhuenda García, Yolanda
Revista:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Año de publicación: 2008

Volumen: 32

Número: 2

Páginas: 177-198

Tipo: Artículo

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Otras publicaciones en: Sort: Statistics and Operations Research Transactions

Resumen

The main goal of this paper is to investigate how to estimate sampling design variances of model-based and model-assisted small area estimators in a complex survey sampling setup. For this sake, the Spanish Labour Force Survey is considered. Sample and aggregated data are taken from the Canary Islands in the second trimester of 2003 in order to obtain some small area estimators of ILO unemployment totals. Several problems arising from the application of standard small area estimation procedures to the survey are described. It is shown that standard variance estimators based on explicit formulas are not applicable in strict sense, since the assumptions under which they are derived do not hold. In addition two resampling techniques, bootstrap and jackknife are considered. These methods treat all the considered estimators in the same manner and therefore they can be used as performance measures to compare them. From the analysis of the obtained results, some recommendations are given.

Referencias bibliográficas

  • Das, K., Jiang, J. and Rao, J. N. K. (2001). Mean squared error of empirical predictor. The Annals of Statistics, 32, 818-840.
  • Deville J. C. and Särndal C. E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Society, 87, 376-382.
  • Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.
  • Efron, B. and Tibshirani, R. J. (1998). An Introduction to the Bootstrap. Chapman & Hall/CRC.
  • Fay, R. E. and Herriot, R. A. (1979). Estimates of income for Small Places: An Application of James-Stein Procedures to Census Data. Journal of the American Statistical Association, 74, 269-277.
  • Jiang J. and Lahiri P. (2006). Mixed model prediction and small area estimation. Test, 15, 1-96.
  • Lahiri, P. (2003). On the impact of bootstrap in survey sampling and small-area estimation. Statistical Science, 18, 199-210.
  • McCarthy, P. J. and Snowden, C. B.] (1985). The bootstrap and finite population sampling. In Vital and Health Statistics 2-95. Public Health Service Publication 85-1369, U.S. Government Printing Office, Washington.
  • Miller, R. G. (1964). A trust worthy jackknife. Annals of Mathematical Statistics, 35, 1594-1605.
  • Rao, J. N. K. and Wu, C.-F. J.] (1988). Resampling inference with complex survey data. Journal of the American Statistical Association, 83, 231-241.
  • Rao, J. N. K. (2003). Small Area Estimation. John Wiley.
  • Rao, J. N. K. and Tausi, M. (2004). Estimating function jackknife variance estimators under stratified multistage sampling. Communications in Statistic. Theory and methods, 33, 2087-2095.
  • Rust, K. F. and Rao, J. N. K. (1996) Variance estimation for complex surveys using replication techniques. Statistical Methods in Medical Research, 5, 283-310.
  • Särndal, C.-E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling, Springer-Verlag.
  • Shao, J. and Tu, D. (1995). The Jackknife and the Bootstrap. Springer-Verlag.
  • Shao, J. (2003). Impact of bootstrap on sample surveys. Statistical Science, 18, 191-198.
  • Sitter, R. R. (1992). A resampling procedure for complex survey data. Journal of the American Statistical Association, 87, 755-765.
  • Prasad, N. G. N. and Rao, J. N. K. (1990). The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163-171.
  • Prasad, N. G. N. and Rao, J. N. K. (1999). On robust small area estimation using a simple random effects model. Survey Methodology, 25, 67-72.
  • Quenouille, M. (1949). Approximation tests of correlation in time series. Journal of the Royal Statistical Society, Series B, 11, 18-84.
  • Tukey, J. (1958). Bias and confidence in not quite large samples. Annals of Mathematical Statistics, 29, 614.
  • You, Y. and Rao J. N. K. (2002). A pseudo-empirical best linear unbiased prediction approach to small-area estimation using survey weights. Survey Methodology, 30, 431-439.
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