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Quality and Quantity

, 42:427 | Cite as

Successive Sampling to Estimate Quantiles with P-Auxiliary Variables

  • María Del Mar Rueda
  • Juan Francisco Muñoz
  • Antonio Arcos
Article

Abstract

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the previous occasion. A multivariate ratio estimator from the matched portion is used to provide the optimum estimate of a quantile by weighting the estimates inversely to derived optimum weights. Its properties are studied under large–sample approximation and the expressions of the variances are established. The behavior of these asymptotic variances is analyzed on the basis of data from natural populations. A simulation study is also used to measure the precision of the proposed estimator.

Keywords

longitudinal surveys successive sampling matched and unmatched samples distribution function quantiles 

References

  1. Adhvaryu D. (1978). Successive sampling using multi-auxiliary information. Sankhya 40: 167–173Google Scholar
  2. Allen J., Singh H. P., Singh S. & Smarandache F. (2002). A general class of of population median using two auxiliary variables in double sampling. INTERSTAT. INTERSTAT — Statistics on the Internet. Blacksburg, USA: Virginia Polytechnic Institute and State University.Google Scholar
  3. Arnab R., Okafor F.C. (1992). A note on double sampling over two occasions. Journal of Statistics 8: 9–18Google Scholar
  4. Chambers R.L., Dunstan R. (1986). Estimating distribution functions from survey data. Biometrika 73: 597–604CrossRefGoogle Scholar
  5. Cochran W.G. (1977). Sampling Techniques, 3rd edn. New York, WileyGoogle Scholar
  6. Cramer H. (1946). Mathematical Methods of Statistics. Princeton, Princenton University PressGoogle Scholar
  7. Eckler A.R.(1955). Rotation sampling. The Annals of Mathematical Statistics 26: 664–685CrossRefGoogle Scholar
  8. Eurostat, (2000). Low-wage employees in EU countries. In: Statistics in Focus: Population and Social Conditions. Theme 3-11/2000. Luxembourg: Office for Official Publications of the EC.Google Scholar
  9. Gordon L. (1983). Successive sampling in finite populations. The Annals of Statistics 11: 702–706CrossRefGoogle Scholar
  10. Gross S.T.(1980). Median estimation in sample survey. In: Proceedings Survey and Research Method Section American Statistical Association 181–184Google Scholar
  11. Jessen R.J. (1942). Statistical investigation of a sample survey for obtaining farm facts. Iowa Agricultural Experiment Statistical Research Bulletin 304Google Scholar
  12. Koenker R., Hallock K.F.(2001). Quantile regression. Journal of Economics 15(4): 143–156Google Scholar
  13. Kuk A., Mak T.K.(1989). Median estimation in the presence of auxiliary information. Journal of the Royal Statistical Society B 51: 261–269Google Scholar
  14. Mak T.K., Kuk A.Y.C. (1993). A new method for estimating finite–population quantiles using auxiliary information. The Canadian Journal of Statistics 25: 29–38CrossRefGoogle Scholar
  15. Narain R.D.(1953). On the recurrence formula in sampling on successive occasions. Journal of the Indian Society of Agricultural Statistics 5: 96–99Google Scholar
  16. Olkin I. (1958). Multivariate ratio estimation for finite population. Biometrika 45: 154–165Google Scholar
  17. Patterson H.D.(1950). Sampling on successive occasions with partial replacement of units. Journal of the Royal Statistical Society B 12: 241–255Google Scholar
  18. Rao J.N.K., Kovar J.G., Mantel H.J.(1990). On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77(2): 365–375CrossRefGoogle Scholar
  19. Royal R.M., Cumberland W.G.(1981). An empirical study of the ratio estimator and estimators of its variance. Journal of the American Statistical Association 76: 66–77CrossRefGoogle Scholar
  20. Rueda M., Arcos A., Artés E. (1998). Quantile interval estimation in finite population using a multivariate ratio estimator. Metrika 47: 203–213CrossRefGoogle Scholar
  21. Ruspini E. (1999). Longitudinal research and the analysis of social change. Quality and Quantity 33: 219–227CrossRefGoogle Scholar
  22. Sedransk J., Meyer J. (1978). Confidence intervals for the quantiles of a finite simple random and stratified simple random sampling. Journal of the Royal Statistical Society B 40(2): 239–252Google Scholar
  23. Sedransk J. & Smith P.J.(1988). Inference for finite population quantiles. In P. R. Krishnaiah & C. R. Rao (eds.), Handbook of Statistics Vol. 6, Chap. 11, North-Holland. pp. 267–289Google Scholar
  24. Singh S., Joarder A.H., Tracy D.S.(2001). Median estimation using double sampling. Australlian and New Zealand Jourlnal of Statistics 43: 33–46CrossRefGoogle Scholar
  25. Singh H. P., Singh H.P., Singh V.P.(1992). A generalized efficient class of estimators of population mean in two phase and successive sampling. International Journal of Management Systems 8(2): 173–183Google Scholar
  26. Singh S., Srivastrava A.K.(1973). Use of auxiliary information in two stage sampling. Journal of Indian Society of Agricultural Statistic 25: 101–104Google Scholar
  27. Singh S. (2003). Advanced Sampling Theory With Applications: How Michael “Selected” Amy. The Netherlands, Kluwer Academic Publisher, pp. 1–1247Google Scholar
  28. Solga H. (2001). Longitudinal surveys and the study of occupational mobility: panel and retrospective design in comparison. Quality and Quantity 35: 291–309CrossRefGoogle Scholar
  29. Valliant R., Dorfman A.H., Royall R.M.(2000). Finite Population Sampling and Inference: A Prediction Approach Wiley Series in Probability and Statistics, Survey Methodology Section. New York, WileyGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • María Del Mar Rueda
    • 1
  • Juan Francisco Muñoz
    • 2
  • Antonio Arcos
    • 1
  1. 1.Department of Statistics and Operational Research, Facultad de CienciasUniversity of GranadaGranadaSpain
  2. 2.Department of Quantitative Methods in Economics and Business, Facultad de Ciencias Económicas y EmpresarialesUniversity of GranadaGranadaSpain

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