Abstract
The estimation of the finite population distribution function under several sampling strategies based on a PPS cluster sampling, i.e., with cluster selection probabilities proportional to size, is studied. For the estimation of population means and totals, it is well-known that this type of strategies gives good results if the cluster selection probabilities are proportional to the total of the variable under study or to a related auxiliary variable over the cluster. It is proved that, for the estimation of the distribution function using cluster sampling, this solution is not good in general and, under an appropriate criteria, the optimal cluster selection probabilities that minimize the variance of the estimation, is obtained. This methodology is applied to two classical PPS sampling strategies: sampling with replacement, with the Hansen-Hurwitz estimator, and random groups sampling with the Rao-Hartley-Cochran estimator. Finally a small simulation to compare the efficiency of this approach with other methods is presented.
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References
Chambers, R., Dorfman, A., andHall, P. (1992). Properties of estimators of the finite population distribution function.Biometrika, 79:577–582.
Chambers, R., andDunstan, R. (1986). Estimating distribution functions from survey data.Biometrika, 73:597–604.
Hansen, M. andHurwitz, W. (1943). On the theory of sampling from finite populations.Annals of Mathematical Statistics, 14:333–362.
Kuk, A. (1988). Estimation of distribution functions and medians under sampling with unequal probabilities.Biometrika, 75:97–103.
Rao, J. (1994). Estimating totals and distributions functions using auxiliary information in the estimation stage.Journal of Official Statistics, 10:153–166.
Rao, J., Hartley, H., andCochran, W. (1962). A simple procedure of unequal probability sampling without replacement.Journal of the Royal Statistical Society B, 24:482–491.
Rao, J., Kovar, J., andMantel, H. (1990). On estimating distribution functions and quantiles from survey data using auxiliary information.Biometrika, 77:365–375.
Särndal, C., Swensson, B., andWretman, J. (1992).Model Assisted Survey Sampling. Springer-Verlag, New York, Inc.
Welsh, A. andRonchetti, E. (1998). Bias-calibrated estimation from sample surveys containing outliers.Journal of the Royal Statistical Society B 60(2):413–428.
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Mayor, J.A. Optimal cluster selection probabilities to estimate the finite population distribution function under PPS cluster sampling. Test 11, 73–88 (2002). https://doi.org/10.1007/BF02595730
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DOI: https://doi.org/10.1007/BF02595730
Key Words
- Finite population distribution function
- selection probabilities proportional to size
- optimal cluster selection probabilities
- random groups