Journal of Statistical Theory and Practice

, Volume 5, Issue 1, pp 147–160 | Cite as

Variance Approximation Under Balanced Sampling Plans Excluding Adjacent Units

  • James H. WrightEmail author
  • John Stufken


Hedayat, Rao and Stufken (1988a, 1988b) first introduced balanced sampling plans for the exclusion of contiguous units. Sampling plans that exclude the selection of contiguous units within a given sample, while maintaining a constant second-order inclusion probability for non-contiguous units, were investigated for finite populations of N units arranged in a circular, one-dimensional ordering. Although significant advancements have been achieved concerning the generalization and existence of such sampling plans for finite, one-dimensional populations, many other aspects of these plans warrant further investigation. We present the results of an investigation of three biased estimators of the variance of the Horvitz-Thompson estimator of the population mean under such plans.


Variance estimation Balanced sampling plans excluding adjacent units Polygonal designs Circularly and linearly ordered populations Finite population sampling 

AMS Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dukes, P.J., Ling, A.C.H., 2009. Existence of balanced sampling plans avoiding cyclic distances. Metrika, 70, 131–140.MathSciNetCrossRefGoogle Scholar
  2. Hedayat, A.S., Rao, C.R., Stufken, J., 1988. Sampling plans excluding contiguous units. J. Statist. Plann. Inference, 19, 159–170.MathSciNetCrossRefGoogle Scholar
  3. Hedayat, A.S., Rao, C.R., Stufken, J., 1988. Designs in survey sampling avoiding contiguous units. In Handbook of Statistics, Vol. 6, Krishnaiah, P.R., and Rao, C.R. (Editors), Elsevier, Amsterdam, pp. 575–583.Google Scholar
  4. 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.MathSciNetzbMATHGoogle Scholar
  5. Stufken, J., Song, S.Y., See, K., Driessel, K.R., 1999. Polygonal designs: some existence and non-existence results. J. Statist. Plann. Inference, 77, 155–166.MathSciNetCrossRefGoogle Scholar
  6. Stufken, J., Wright, J.H., 2001. Polygonal designs with blocks of size k ≤ 10. Metrika, 54, 179–184.MathSciNetCrossRefGoogle Scholar
  7. Wright, J.H., 2008. Two-dimensional balanced sampling plans excluding adjacent units. J. Statist. Plann. Inference, 138, 145–153.MathSciNetCrossRefGoogle Scholar
  8. Wright, J.H., Stufken, J., 2008. New balanced sampling plans excluding adjacent units. J. Statist. Plann. Inference, 138, 3326–3335.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.AstraZeneca Pharmaceuticals LPWilmingtonUSA
  2. 2.Department of StatisticsUniversity of GeorgiaAthensUSA

Personalised recommendations