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Metrika

, Volume 41, Issue 1, pp 355–362 | Cite as

Model assisted survey sampling strategy in two phases

  • Arijit Chaudhuri
  • Debesh Roy
Article

Abstract

Postulating a super-population regression model connecting a size variable, a cheaply measurable variable and an expensively observable variable of interest, an asymptotically optimal double sampling strategy to estimate the survey population total of the third variable is specified. To render it practicable, unknown model-parameters in the optimal estimator are replaced by appropriate statistics. The resulting generalized regression estimator is then shown to have a model-cum-asymptotic design based expected square error equal to that of the asymptotically optimum estimator itself. An estimator for design variance of the estimator is also proposed.

Key Words and Phrases

Asymptotic analysis double sampling generalized regression estimator optimal strategy survey population variance estimation 

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References

  1. Brewer KRW (1979) A class of robust sampling designs for large-scale surveys. Jour Amer Statist Assoc 74: 911–915Google Scholar
  2. Chaudhuri A, Adhikari AK (1983) On optimality of double sampling strategies with varying probabilities. Jour Statist Plan and Inf 8: 257–265Google Scholar
  3. Chaudhuri A, Adhikari AK (1985) Some results on admissibility and uniform admissibility in double sampling. Jour Statist Plan and Inf 12: 199–202Google Scholar
  4. Cramer H (1966) Mathematical methods of statistics. Princepon Univ PressGoogle Scholar
  5. Fuller WA, Isaki CT (1981) Survey design under superpopulation models. In: Current topics in survey sampling. Krewski D, Platek R, Rao JNK (Eds) Academic Press, NY 199–226Google Scholar
  6. Godambe VP, Joshi VM (1965) Admissibility and bayes estimation in sampling finite populations. I. Ann Math Statist 36: 1707–1722Google Scholar
  7. Godambe VP, Thompson ME (1977) Robust near optimal estimation in survey practice. Bull Int Statist Inst 47, 3: 129–146Google Scholar
  8. Horvitz DG, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. Jour Amer Statist Assoc 47: 663–685Google Scholar
  9. Isaki CT, Fuller WA (1982) Survey design under the regression superpopulation model. Jour Amer Statist Assoc 7: 89–96Google Scholar
  10. Mukerjee R, Chaudhuri A (1990) Asymptotic optimality of double sampling plans employing generalized regression estimators. Jour Statist Plan and Inf 26: 173–183Google Scholar
  11. Rao JNK, Bellhouse DR (1978) Optimal estimation of a finite population mean under generalized random permutation models. Jour Statist Plan and Inf 2: 125–141Google Scholar
  12. Robinson PM, Särndal CE (1983) Asymptotic properties of the generalized regression estimator in probability sampling. Sankhya B, 45: 240–248Google Scholar
  13. Särndal CE (1980) On π-inverse weighting versus best linear weighting in probability sampling. Biometrika 67: 634–650Google Scholar
  14. Särndal CE (1982) Implications of survey design for genralized regression estimation of lienar functions. Jour Statist Plan and Inf 7: 155–170Google Scholar
  15. Särndal CE, Swensson BE, Wretman JH (1992) Model assisted survey sampling. Springer VerlagGoogle Scholar
  16. Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. Jour Roy Statist Soc B 15: 253–261Google Scholar

Copyright information

© Physica-Verlag 1994

Authors and Affiliations

  • Arijit Chaudhuri
    • 1
  • Debesh Roy
    • 2
  1. 1.Indian Statistical InstituteCalcuttaIndia
  2. 2.Residency CollegeCalcuttaIndia

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