A Class of Hartley-Ross-Type Estimators for Population Mean in Adaptive and Stratified Adaptive Cluster Sampling

Research Paper
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Abstract

In this article, we propose a class of Hartley-Ross-type unbiased estimators of finite population mean under adaptive cluster sampling and stratified adaptive cluster sampling. The estimators utilize information on known parameters of the auxiliary variable. The variances of proposed class of unbiased estimators are obtained up to first degree of approximation. Proposed estimators are more efficient than the usual mean estimator, ratio, and modified ratio estimators in adaptive cluster sampling and stratified adaptive cluster sampling under certain realistic conditions. Simulation study considering different populations is carried out to support the theoretical findings.

Keywords

Adaptive cluster sampling Auxiliary variable Hartley-Ross Bias Mean square error 

Notes

Acknowledgements

The authors are thankful to the editor and anonymous referees for their valuable suggestions, which helped to improve the article.

References

  1. Chao CT, Dryver AL, Chiang TZ (2011) Leveraging the Rao–Blackwell theorem to improve ratio estimators in adaptive cluster sampling. Environ Ecol Stat 18:543–568MathSciNetCrossRefGoogle Scholar
  2. Christman MC, Lan F (2001) Inverse adaptive cluster sampling. Biometrics 57:1096–1105MathSciNetCrossRefMATHGoogle Scholar
  3. Chutiman N (2010) A new ratio estimator in stratified adaptive cluster sampling. Thail Stat 8:223–233MATHGoogle Scholar
  4. Chutiman N (2013a) Adaptive cluster sampling using auxiliary variable. J Math Stat 9(3):249–255CrossRefGoogle Scholar
  5. Chutiman N, Chiangpradit M, Suraphee S (2013) A new estimator using auxiliary information in stratified adaptive cluster sampling. Open J Stat 3:278–282CrossRefMATHGoogle Scholar
  6. Dryver AL, Chao CT (2007) Ratio estimators in adaptive cluster sampling. Environmetrics 18:607–620MathSciNetCrossRefGoogle Scholar
  7. Dryver AL, Thompson SK (2005) Improved unbiased estimators in adaptive cluster sampling. J R Stat Soc 67:157–166MathSciNetCrossRefMATHGoogle Scholar
  8. Dryver AL, Nethran U, Smith DR (2012) Partial systematic adaptive cluster sampling. Environmetrics 23:306–316MathSciNetCrossRefGoogle Scholar
  9. Félix-Medina MH, Thompson SK (2004) Adaptive cluster double sampling. Biometrica 91:877–891MathSciNetCrossRefMATHGoogle Scholar
  10. Gattone SA, Mohamed E, Dryver AL, Munnich RT (2016) Adaptive cluster sampling for negatively correlated data. Environmetrics 27:103–113MathSciNetCrossRefGoogle Scholar
  11. Hartley HO, Ross A (1954) Unbiased ratio estimators. Nature 174:270–272CrossRefGoogle Scholar
  12. Lin F, Chao C (2014) Variances and variance estimators of the improved ratio estimators under adaptive cluster sampling. Environ Ecol Stat 21:285–311MathSciNetCrossRefGoogle Scholar
  13. Muttlak HA, Khan A (2002) Adjusted two-stage adaptive cluster sampling. Environ Ecol Stat 9:111–120MathSciNetCrossRefMATHGoogle Scholar
  14. Singh HP, Sharma B, Tailor R (2014) Hartley–Ross type estimators for population mean using known parameters of auxiliary variate. Commun Stat Theory Methods 43:547–565MathSciNetCrossRefMATHGoogle Scholar
  15. Smith DR, Conroy MJ, Brakhage DH (1995) Efficiency of adaptive cluster sampling for estimating density of wintering waterfowl. Biometrics 51:777–788CrossRefGoogle Scholar
  16. Thompson SK (1990) Adaptive cluster sampling. J Am Stat Assoc 85:1050–1059MathSciNetCrossRefMATHGoogle Scholar
  17. Thompson SK (1991) Stratified adaptive cluster sampling. Biometrika 78:389–397MathSciNetCrossRefGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of StatisticsQuaid-i-Azam UniversityIslamabadPakistan

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