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Improved Classes of Estimators for Population Mean Using Information on Auxiliary Character Under Double Sampling the Non-respondents

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Abstract

In this paper, improved classes of estimators have been proposed for estimating the population means of the study character using the information on auxiliary character and attribute in the presence of non-response on study character only and their properties are studied. The conditions for attaining the minimum mean square error of the proposed classes of estimators are also given. Further, the problem has been extended to the two phase sampling when the population proportion and mean of auxiliary character are not known. Two wider classes of generalized estimators under these conditions have been proposed and their properties are studied. The expressions of optimum sample size for first phase, second phase and sub-sampling fraction have been obtained in case of fixed cost as well as for fixed precision. Theoretical and empirical studies have been made with relevant estimators to show the efficiency of the proposed classes of estimators with real data set from census handbook published by Government of India.

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References

  1. Hansen MH, Hurwitz WN (1946) The problem of non-response in sample surveys. J Am Stat Assoc 41:517–529

    Article  Google Scholar 

  2. Cochran WG (1942) Sampling theory when sampling units are of unequal sizes. J Am Stat Assoc 37:199–212

    Article  Google Scholar 

  3. Tripathi TP, Das AK, Khare BB (1994) Use of auxiliary information in sample surveys-a review. Aligarh J Stat 14:79–134

    Google Scholar 

  4. Khare BB (2003) Use of auxiliary information in sample surveys up to 2000—a review. In: Sen DK, Mishra PK (eds) Mathematics and statistics in engineering, biotechnology and science. M/S Centre of Bio-Mathematical Studies. Ankara, Turkey, pp 76–87

  5. Rao PSRS (1986) Ratio estimation with subsampling the nonrespondents. Surv Methodol 12:217–230

    Google Scholar 

  6. Khare BB, Srivastava S (1993) Estimation of population mean using auxiliary character in presence of non-response. Natl Acad Sci Lett India 16:111–114

    Google Scholar 

  7. Rao PSRS (1990) Regression estimators with subsampling of nonrespondents. In: Liepins Gunar E, Uppuluri VRR (eds) Data quality control, theory and pragmatics. Marcel Dekker, New York, pp 191–208

    Google Scholar 

  8. Khare BB, Srivastava S (2000) Generalised estimators for population mean in presence of nonresponse. Int J Math Stat Sci 9:75–87

    Google Scholar 

  9. Naik VD, Gupta PC (1996) A note on estimation of mean with known population proportion of an auxiliary character. J Indian Soc Agric Stat 48(2):151–158

    Google Scholar 

  10. Jhajj HS, Sharma MK, Grover LK (2006) A family of estimators of population mean using auxiliary attribute. Pak J Stat 22(1):43–50

    Google Scholar 

  11. Abd-Elfattah AM, El-Sherpieny EA, Mohamed SM, Abdou OF (2010) Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute. Appl Math Comput 215:4198–4202

    Article  Google Scholar 

  12. Shabbir J, Gupta S (2010) Estimation of the finite population mean in two phase sampling when auxiliary variables are attributes. Hacett J Math Stat 39(1):121–129

    Google Scholar 

  13. Grover LK, Kaur P (2011) An improved exponential estimator of finite population mean in simple random sampling using an auxiliary attribute. Appl Math Comput 218:3093–3099

    Article  Google Scholar 

  14. Singh HP, Solanki RS (2012) Improved estimation of population mean in simple random sampling using information on auxiliary attribute. Appl Math Comput 218:7798–7812

    Article  Google Scholar 

  15. Cochran WG (1977) Sampling techniques. Wiley, New York

    Google Scholar 

  16. Khare BB, Sinha RR (2002) General class of two phase sampling estimators for the population mean using an auxiliary character in the presence of non-response. In: Proceedings of the 5th international symposium on optimization and statistics, pp 233–245

  17. Khare BB, Srivastava S (1995) Study of conventional and alternative two phase sampling ratio, product and regression estimators in presence of non-response. Proc Natl Acad Sci India 65(A)(II):195–203

    Google Scholar 

  18. Khare BB, Srivastava S (2010) Generalized two phase estimators for the population mean in the presence of non-response. Aligarh J Stat 30:39–54

    Google Scholar 

  19. Srivastava S (1993) Some problems on the estimation of population mean using auxiliary character in presence of non-response in sample surveys. Unpublished Ph.D. thesis submitted to B.H.U., Varanasi, India

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Authors and Affiliations

  1. Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, India

    R. R. Sinha & Vinod Kumar

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  1. R. R. Sinha
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  2. Vinod Kumar
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Correspondence to R. R. Sinha.

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Sinha, R.R., Kumar, V. Improved Classes of Estimators for Population Mean Using Information on Auxiliary Character Under Double Sampling the Non-respondents. Natl. Acad. Sci. Lett. 37, 71–79 (2014). https://doi.org/10.1007/s40009-013-0198-z

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  • DOI: https://doi.org/10.1007/s40009-013-0198-z

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