Journal of Statistical Theory and Practice

, Volume 6, Issue 2, pp 274–285 | Cite as

An Efficient Class of Estimators for the Population Mean Using Auxiliary Information in Systematic Sampling

  • Housila P. SinghEmail author
  • Ramkrishna S. Solanki


This article addresses the problem of estimating the population mean in systematic sampling using information on an auxiliary variable. A class of estimators for the population mean is defined with its properties under large sample approximation. It has been shown that the proposed class of estimators is better than the usual unbiased estimator, Swain (1964) estimator, Shukla (1971) estimator, and usual regression estimator. The results have been illustrated through an empirical study.

AMS Subject Classification



Auxiliary variable Bias Mean square error Study variable Systematic sampling 


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  1. Banarasi, S. N. S., Kushwaha, and K.S. Kushwaha. 1993. A class of ratio product and difference (RPD) estimators in systematic sampling. Microelectron Reliab., 33(4), 455–457.CrossRefGoogle Scholar
  2. Cochran, W. G. 1946. Relative efficiency of systematic and stratified random samples for a certain class of populations. Ann. Math. Stat., 17, 164–177.CrossRefGoogle Scholar
  3. Cochran, W. G. 1977. Sampling techniques, 34rd ed. New York, NY, John Wiley and Sons.zbMATHGoogle Scholar
  4. Gautschi, W. 1957. Some remarks on systematic sampling. Ann. Math. Stat., 28, 385–394.MathSciNetCrossRefGoogle Scholar
  5. Griffth, A. L. 1945–1946. The efficiency of enumerations. Forest-Research Institute, Dehra Dun. Indian Forest Leaflets 83–93.Google Scholar
  6. Gupta, S., and J. Shabbir. 2007. On the use of transformed auxiliary variables in estimating population mean. J. Stat. Plan. Inference 137(5), 1606–1611.CrossRefGoogle Scholar
  7. Gupta, S., Shabbir, J., 2008. On improvement in estimating the population mean in simple random sampling. J. Appl. Stat., 35(5), 559–566.MathSciNetCrossRefGoogle Scholar
  8. Hajeck, J. 1959. Optimum strategy and other problems in probability sampling. Casopis pro Pestovani Matematiky 84, 387–423.MathSciNetGoogle Scholar
  9. Hasel, A. A. 1942. Estimation of volume of timber stands by strip sampling. Ann. Math. Stat., 13, 179–206.MathSciNetCrossRefGoogle Scholar
  10. Iachan, R. 1982. Systematic sampling: A critical review. Int. Stat. Rev. 50, 293–303.MathSciNetCrossRefGoogle Scholar
  11. Jhajj, H. S., M. K. Sharma, and L. K. Grover. 2006a. Dual of ratio estimators of finite population mean obtained using lineal transformation to auxiliary variable. J. Jpn. Stat. Soc., 36(1), 107–119.CrossRefGoogle Scholar
  12. Jhajj, H. S., M. K. Sharma, and L. K. Grover. 2006b. A family of estimators of population mean using information on auxiliary attribute. Pak. J. Stat., 22(1), 43–50.MathSciNetzbMATHGoogle Scholar
  13. Koyuncu, N., and C. Kadilar. 2009. Ratio and product estimators in stratified random sampling. J. Stat. Plan. Inference, 139, 2552–2558.MathSciNetCrossRefGoogle Scholar
  14. Koyuncu, N., and C. Kadilar. 2010a. On improvement in estimating population mean in stratified random sampling. J. Appl. Stat., 37(6), 999–1013.MathSciNetCrossRefGoogle Scholar
  15. Koyuncu, N., and C. Kadilar. 2010b. On the family of estimators of population mean in stratified random sampling. Pak. J. Stat., 26(2), 427–443.MathSciNetzbMATHGoogle Scholar
  16. Kushwaha, K. S., and H. P. Singh. 1989. Class of almost unbiased ratio and product estimators in systematic sampling. J. Ind. Soc. Agric. Stat., 41(2), 193–205.MathSciNetGoogle Scholar
  17. Murthy, M. N. 1967. Sampling theory and methods. Calcutta, India, Statistical Publishing Society.zbMATHGoogle Scholar
  18. Obsborne, J. G. 1942. Sampling errors of systematic and random surveys of cover-types areas. J. Am. Stat. Assoc., 37, 256–264.CrossRefGoogle Scholar
  19. Prasad, B. 1989. Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Commun. Stat., Theory Methods, 18, 379–392.MathSciNetCrossRefGoogle Scholar
  20. Quenouille, M. H. 1956. Notes on bias in estimation. Biometrika 43, 353–360.MathSciNetCrossRefGoogle Scholar
  21. Raj, D. 1968. Sampling theory. New Delhi, India, Tata-Mcgraw Hill.zbMATHGoogle Scholar
  22. Searls, D. T. 1964. The utilization of known coefficient of variation in the estimation procedure. J. Am. Stat. Assoc., 59, 1225–1226.CrossRefGoogle Scholar
  23. Shabbir, J., and S. Gupta. 2011. On estimating the finite population mean in simple and stratified random sampling. Commun. Stat. Theory Methods, 40(2), 199–212.MathSciNetCrossRefGoogle Scholar
  24. Shabbir, J., and S. Gupta. 2005. Improved ratio estimators in stratified sampling. Am. J. Math. Manage. Sci., 25(3/4), 293–311.MathSciNetzbMATHGoogle Scholar
  25. Shabbir, J., and S. Gupta. 2006. A new estimator of population mean in stratified sampling. Commun. Stat. Theory Methods, 35(7), 1201–1209.MathSciNetCrossRefGoogle Scholar
  26. Shukla, N. D., 1971. Systematic sampling and product method of estimation. Proceeding of all India Seminar on Demography and Statistics, B.H.U., Varanasi, India.Google Scholar
  27. Singh, H. P., and G. K. Vishwakarma. 2008. A family of estimators of population mean using auxiliary information in stratified sampling. Commun. Stat. Theory Methods, 37, 1038–1050.CrossRefGoogle Scholar
  28. Singh, H. P., and G. K. Vishwakarma. 2010. A general procedure for estimating the population mean in stratified sampling using auxiliary information. Metron 67(1), 47–65.MathSciNetCrossRefGoogle Scholar
  29. Singh, D., and P. Singh. 1977. New systematic sampling. J. Stat. Plan. Inference 1, 163–179.MathSciNetCrossRefGoogle Scholar
  30. Singh, H. P., 1986a. Estimator of ratio, product and mean using auxiliary information in sample surveys. Aligarh. J. Stat., 6, 32–44.zbMATHGoogle Scholar
  31. Singh, H. P. 1986b. A generalized class of estimators of ratio, product and mean using supplementary information on an auxiliary character in PPSWR sampling scheme. Gujarat Stat. Rev., 13(2), 1–30.MathSciNetGoogle Scholar
  32. Singh, R., and H. P. Singh. 1998. Almost unbiased ratio and product type estimators in systematic sampling. Questiio, 22(3), 403–416.MathSciNetzbMATHGoogle Scholar
  33. Singh, S. 2003. Advanced sampling theory with applications. How Michael selected Amy. Dordrecht, The Netherlands, Kluwer Academic Publishers.CrossRefGoogle Scholar
  34. Singh, S., and R. Singh. 1993. A new method: Almost separation of bias precipitates in sample surveys. J. Ind. Stat. Assoc., 31, 99–105.MathSciNetGoogle Scholar
  35. Sukhatme, P. V., B. V. Sukhatme, S. Sukhatme, and C. Asok. 1984. Sampling theory of surveys with applications, 3rd ed. Ames, Iowa State University Press.zbMATHGoogle Scholar
  36. Swain, A. K. P. C. 1964. The use of systematic sampling in ratio estimate. J. Ind. Stat. Assoc. 2(213), 160–164.MathSciNetGoogle Scholar
  37. Swain, A. K. P. C. 2003. Finite population sampling—Theory and Methods. New Delhi, India, South Asian PublishersGoogle Scholar
  38. Upadhyaya, L. N., H. P. Singh, and J. W. E. Vos. 1985. On the estimation of population means and ratios using supplementary information. Stat. Neerlandica, 39(3), 309–318.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.School of Studies in StatisticsVikram UniversityUjjainIndia

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