Skip to main content
SpringerLink
Log in

Existence of balanced sampling plans avoiding cyclic distances

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

This article considers balanced sampling plans avoiding adjacent units. It is shown, using linear algebraic and design theoretic tools, that such plans exist for all sufficiently large populations. More generally, if any set of m circular distances is to be avoided in balanced sampling with subsets of size k, then such a plan exists, provided the population size N is at least mk 3.

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

  • Bryant D, Chang Y, Rodger CA, Wei R (2002) Two-dimensional balanced sampling plans excluding contiguous units. Comm Statist Theory Methods 31: 1441–1455

    Article  MATH  MathSciNet  Google Scholar 

  • Carnicer JM, Goodman TNT, Peña JM (1999) Linear conditions for positive determinants. Linear Algebra Appl 292: 39–59

    Article  MATH  MathSciNet  Google Scholar 

  • Colbourn CJ, Dinitz JH (2007) Handbook of combinatorial designs, 2nd ed. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Colbourn CJ, Ling ACH (1998) A class of partial triple systems with application in survey sampling. Commun Stat Theory Methods 27: 1009–1018

    Article  MATH  MathSciNet  Google Scholar 

  • Colbourn CJ, Ling ACH (1999) Balanced sampling plans with block size four excluding contiguous units. Australas J Combin 20: 37–46

    Article  MATH  MathSciNet  Google Scholar 

  • Hedayat AS, Rao CR, Stufken J (1988a) Designs in survey sampling avoiding contiguous units. In: Krishnaiah PR, Rao CR(eds) Handbook of statistics 6: sampling. North-Holland, Amsterdam, pp 575–583

    Google Scholar 

  • Hedayat AS, Rao CR, Stufken J (1988b) Sampling plans excluding contiguous units. J Statist Plann Inference 19: 159–170

    Article  MATH  MathSciNet  Google Scholar 

  • See K, Song SY, Stufken J (1997) On a class of partially balanced incomplete block designs with applications in survey sampling. Commun Statist Theory Methods 26: 1–13

    Article  MATH  MathSciNet  Google Scholar 

  • Stufken J (1993) Combinatorial and statistical aspects of sampling plans to avoid the selection of adjacent units. J Combin Inform System Sci 18: 81–92

    MathSciNet  Google Scholar 

  • Stufken J, Song SY, See K, Driessel KR (1999) Polygonal designs: some existence and non-existence results. J Statist Plann Inference 77: 155–166

    Article  MATH  MathSciNet  Google Scholar 

  • Stufken J, Wrignt JH (2001) Polygonal designs with blocks of size k  ≤  10. Metrika 54: 179–184

    Article  MATH  MathSciNet  Google Scholar 

  • West DB (2001) Introduction to Graph Theory, 2nd ed. Prentice Hall, Boston

    Google Scholar 

  • Wright JH, Stufken J (2007) New balanced sampling plans excluding adjacent units (preprint)

Download references

Author information

Authors and Affiliations

  1. University of Victoria, Victoria, BC, V8W 3P4, Canada

    Peter J. Dukes

  2. University of Vermont, Burlington, VT, 05405, USA

    Alan C. H. Ling

Authors
  1. Peter J. Dukes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan C. H. Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter J. Dukes.

Additional information

Research of the Peter J. Dukes is supported by NSERC.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dukes, P.J., Ling, A.C.H. Existence of balanced sampling plans avoiding cyclic distances. Metrika 70, 131–140 (2009). https://doi.org/10.1007/s00184-008-0182-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-008-0182-7

Keywords

Search

Navigation