Advertisement

Near Optimum Allocations in Stratified Sampling

Article

Abstract

In this paper, we shall discuss the problem of optimum allocation of sample size to strata under the constraints of fixed total sample size and fixed total cost in a general setting. We shall also obtain near-optimum allocations for use in practice. This will result in minor loss of efficiency due to deviations from the optimum. We shall also provide illustrative examples.

AMS Subject Classification

62D05 

Keywords

Stratified sampling Optimum allocation Super population model Near-optimum allocations Deviations from the optimum 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bankier, M.D., 1988. Power allocations: determining sample sizes for sub-national areas. The Amer. Stat., 42, 174–177.Google Scholar
  2. Cochran, W.G., 1977. Sampling Techniques. 3rd edition, Wiley, New York.MATHGoogle Scholar
  3. Government of India, 2008a. Household consumer expenditure in India, 2005–06. NSS 62nd Round, January, 2008.Google Scholar
  4. Government of India, 2008b. Household consumer expenditure in India, 2006–07. NSS 63rd Round, October, 2008.Google Scholar
  5. Gupt, B.K., Rao, T.J., 1997. Stratified PPS sampling and allocation of sample size. J. Ind. Soc. Agr. Stat., 50, 199–208.Google Scholar
  6. Hanurav, T.V., 1965. Optimum Sampling Strategies and Some Related Problems. Ph.D. thesis submitted to the Indian Statistical Institute.Google Scholar
  7. Lehtonen, R., Pahkinen, E., 2004. Practical Methods for Design and Analysis of Complex Surveys. 2nd edition, Wiley.MATHGoogle Scholar
  8. Mahalanobis, P.C., 1944. On large scale sample surveys. Phil. Trans. Roy. Soc., London, Series B, 231, 329–451.CrossRefGoogle Scholar
  9. Murthy, M.N., 1967. Sampling Theory and Methods. Statistical Publishing Society, Calcutta.MATHGoogle Scholar
  10. Neyman, J., 1934. On the two different aspects of the representative method: the method of stratified sampling and the method of purposive selection. J. Roy. Stat. Soc., 97, 558–606.CrossRefGoogle Scholar
  11. Pukelsheim, F., 1997. Efficient rounding of sampling allocations. Stat. Prob. Lett., 35, 141–143.MathSciNetCrossRefGoogle Scholar
  12. Rao, T.J., 1977. Optimum allocation of sample size and prior distributions: a review. Int. Stat. Rev., 45, 173–179.MathSciNetCrossRefGoogle Scholar
  13. Rao, T.J., 1984. Allocation of sample size to strata and related problems. Biom. J., 26, 517–526.CrossRefGoogle Scholar
  14. Rao, T.J., 2001. Some problems in stratified sampling. Bull. Int. Stat. Inst., 53.Google Scholar
  15. Särndal, C.E., Swenson, B., Wretman, J., 1991. Model Assisted Survey Sampling. Springer-Verlag.MATHGoogle Scholar
  16. Tschuprow, A.A., 1923. On the mathematical expectation of the moments of frequency distributions in the case of correlated observations. Metron, 2 (3 and 4), 461–493, 646–683.Google Scholar

Copyright information

© Grace Scientific Publishing 2010

Authors and Affiliations

  1. 1.C. R. Rao Advanced Institute of Mathematics, Statistics and Computer ScienceUniversity of Hyderabad CampusHyderabadIndia

Personalised recommendations