Skip to main content
SpringerLink
Log in

The existence of sampling designs with preassigned inclusion probabilities

  • Publications
  • Published:
Metrika Aims and scope Submit manuscript

Summary

The question of the existence of a sampling design realizing given preassigned inclusion probabilities is treated. The question can be fully answered in the case of inclusion probabilities of first order. If the inclusion probabilities of second order are given it is shown why necessary and sufficient conditions for the existence of a corresponding sampling design can be derived only in very special cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Brewer KRW, Hanif M (1983) Sampling with unequal probabilities. Springer

  • Chaudhuri A (1971) Some sampling schemes to use Horvitz-Thompson estimator in estimating a finite population total. Bull Calcutta Statist Assoc 20:37–66

    MATH  MathSciNet  Google Scholar 

  • Chaudhuri A, Vos JWE (1988) Unified theory and strategies of survey sampling. North-Holland

  • Goldman AJ, Tucker AW (1956) Polyhedral convex cones. In: Annals of Mathematical Studies, No 38, pp 19–40. Princeton University Press

  • Herzel A (1986) Sampling without replacement with unequal probabilities: sample designs with preassigned joint inclusion probabilities of any order. Metron 44:49–68

    MATH  MathSciNet  Google Scholar 

  • Midzuno H (1952) On the sampling system with probability proportional to sum of sizes. Ann Inst Stat Math 3:99–107

    Article  MATH  MathSciNet  Google Scholar 

  • Sampford MR (1967) On sampling without replacement with unequal probabilities of selection. Biometrika 54:499–513

    MathSciNet  Google Scholar 

  • Sinha BK (1973) On sampling schemes to realize preassigned sets of inclusion probabilities of first two orders. Bull Calcutta Statist Assoc 22:89–110

    MATH  Google Scholar 

  • Stoer J, Witzgall CH (1970) Convexity and Optimization in Finite Dimensions I. Springer

  • Tschernikow S (1971) Lineare Ungleichungen. VEB Deutscher Verlag der Wissenschaften

Download references

Author information

Authors and Affiliations

  1. Seminar für Statistik, A5, University of Mannheim, 6800, Mannheim 1

    S. Gabler & R. Schweigkoffer

Authors
  1. S. Gabler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Schweigkoffer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gabler, S., Schweigkoffer, R. The existence of sampling designs with preassigned inclusion probabilities. Metrika 37, 87–96 (1990). https://doi.org/10.1007/BF02613510

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02613510

Key words and phrases

Search

Navigation