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Asymptotic normality for two-stage sampling from a finite population
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  • Published: April 1989

Asymptotic normality for two-stage sampling from a finite population

  • Esbjörn Ohlsson1 

Probability Theory and Related Fields volume 81, pages 341–352 (1989)Cite this article

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  • 10 Citations

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Summary

In this paper we consider two-stage sampling from a finite population, and associated estimators of the population total, in a general setting which includes most two-stage procedures in the literature. The main result gives general conditions for asymptotic normality of the estimators. The proof is based on a martingale central limit theorem. It is indicated how the result can be extended to multi-stage procedures.

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References

  1. Cochran, W.G.: Sampling techniques, 3rd ed. New York: Wiley 1977

    Google Scholar 

  2. Eagleson, G.K.: Martingale convergence to mixtures of infinitely divisible laws. Ann. Probab. 3, 557–562 (1975)

    Google Scholar 

  3. Fuller, W.A.: Regression analysis for sample survey. Sankhyā C 37, 117–132 (1975)

    Google Scholar 

  4. Gordon, L.: Succesive sampling in large finite populations. Ann. Stat. 11, 702–706 (1983)

    Google Scholar 

  5. Hájek, J.: Limiting distributions in simple random sampling from a finite population. Publ. Math. Inst. Hungar. Acad. Sci. 5, 361–374 (1960)

    Google Scholar 

  6. Hájek, J.: Some extensions of the Wald-Wolfowitz-Noether theorem. Ann. Math. Stat. 32, 506–523 (1961)

    Google Scholar 

  7. Hájek, J.: Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann. Math. Stat. 35, 1491–1523 (1964)

    Google Scholar 

  8. Hall, P., Heyde, C.C.: Martingale limit theory and its applications. New York: Academic Press 1980

    Google Scholar 

  9. Holst, L.: Some limit theorems with applications in sampling theory. Ann. Stat. 1, 644–658 (1973)

    Google Scholar 

  10. Högfeldt, P.: Asymptotic theory for Murthy's estimator. Tech. report TRITA-MAT-1980-13, Royal Institute of Technology, Stockholm (1980)

    Google Scholar 

  11. Lanke, J.: On non-negative variance estimators in survey sampling. Sankhyā C36, 33–42 (1974)

    Google Scholar 

  12. Ohlsson, E.: Some remarks on the martingale central limit theorem. Tech. report TRITA-MAT-1985-19, Royal Institute of Technology, Stockholm (1985)

    Google Scholar 

  13. Ohlsson, E.: Asymptotic normality of the Rao-Hartley-Cochran estimator: An application of the martingale CLT. Scand. J. Stat. 13, 17–28 (1986a)

    Google Scholar 

  14. Ohlsson, E.: Asymptotic normality for two-stage sampling from a finite population. Tech. report TRITA-MAT-1986-26, Royal Institute of Technology, Stockholm (1986b)

    Google Scholar 

  15. Raj, Des: Some remarks on a simple procedure of sampling without replacement. J. Am. Stat. Assoc. 61, 391–396 (1966)

    Google Scholar 

  16. Rao, J.N.K., Hartley, H.O., Cochran, W.G.: On a simple procedure of unequal probability sampling without replacement. J. Roy. Stat. Soc. Ser. B24, 482–491 (1962)

    Google Scholar 

  17. Rao, J.N.K.: Unbiased variance estimation for multistage designs. Sankhyā C37, 133–139 (1975)

    Google Scholar 

  18. Rosén, B.: On the central limit theorem for a class of sampling procedures. Z. Wahrscheinlichkeitstheor. Verw. Geb. 7, 103–115 (1967)

    Google Scholar 

  19. Rosén, B.: Asymptotic theory for successive sampling with varying probabilities without replacement, I and II. Ann. Math. Stat. 43, 373–397 and 748–776 (1972)

    Google Scholar 

  20. Rosén, B.: Asymptotic theory for Des Raj's estimator, I and II. Scand. J. Stat. 1, 71–83 and 135–144 (1974)

    Google Scholar 

  21. Sen, P.K.: Limit theorems for an extended coupon collector's problem and for successive subsampling with varying probabilities. Calcutta Stat. Assoc. Bull. 29, 113–132 (1980)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden

    Esbjörn Ohlsson

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  1. Esbjörn Ohlsson
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Ohlsson, E. Asymptotic normality for two-stage sampling from a finite population. Probab. Th. Rel. Fields 81, 341–352 (1989). https://doi.org/10.1007/BF00340058

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  • Received: 05 March 1988

  • Issue Date: April 1989

  • DOI: https://doi.org/10.1007/BF00340058

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Keywords

  • Stochastic Process
  • General Setting
  • General Condition
  • Population Total
  • Probability Theory
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