Estimation of Population Variance Under an Imputation Method in Two-Phase Sampling

  • A. K. Sharma
  • A. K. Singh
Research Article


In this paper, an attempt has been made to reduce the negative effect of random non-response in the estimation procedure of population variance in two-phase sampling. A difference-type imputation method has been considered to reduce the wrong impact of random non-response in the two-phase sampling. To build efficient estimation strategies, information on two auxiliary characters has been used in the estimation of population variance and describes the effectiveness of the proposed estimators; dominant performances of the suggested estimators are compared with the well-known estimators of the population variance under the complete response. Results are explained through empirical studies which are followed by suitable recommendations.


Two-phase Imputation Random non-response Variance estimation Auxiliary variable Bias Mean square error 

Mathematics Subject Classification




The authors are grateful to National Institute of Technology Raipur, Chhattisgarh, and Sri Venkateswara College, University of Delhi, for providing the financial assistance and necessary infrastructure to carry out the present work.


  1. 1.
    Das AK, Tripathi TP (1978) Use of auxiliary information in estimating the finite population variance. Sankhya 34:1–9zbMATHGoogle Scholar
  2. 2.
    Srivstava SK, Jhaji HS (1980) A class of estimators using auxiliary information for estimating finite population variance. Sankhya, C 42:87–96Google Scholar
  3. 3.
    Isaki CT (1983) Variance estimation using auxiliary information. J Am Stat Assoc 78:117–123MathSciNetCrossRefGoogle Scholar
  4. 4.
    Singh RK (1983) Estimation of population variance using ratio and product methods of estimation. Biometika J 25(2):193–200MathSciNetzbMATHGoogle Scholar
  5. 5.
    Upadhyaya LN, Singh HP (1983) Use of auxiliary information in the estimation of population variance. Math Forum 6(2):33–36Google Scholar
  6. 6.
    Tripathi TP, Singh HP, Upadhyaya LN (1988) A generalized method of estimation in double sampling. J Ind Stat Assoc 26:91–101MathSciNetGoogle Scholar
  7. 7.
    Singh S, Joarder AH (1998) Estimation of finite population variance using random non-response in survey sampling. Metrika 47:241–249MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ahmed MS, Abu-Dayyeh W, Hurairah AAO (2003) Some estimators for population variance under two phase sampling. Stat Transit 6(1):143–150Google Scholar
  9. 9.
    Singh HP, Tailor R, Singh S, Kim JM (2011) Estimation of population variance in successive sampling. Qual Quant 45:477–494CrossRefGoogle Scholar
  10. 10.
    Singh HP, Tailor R, Kim JM, Singh S (2012) Families of estimators of finite population variance using a random non-response in survey sampling. Korean J Appl Stat 25(4):681–695CrossRefGoogle Scholar
  11. 11.
    Singh GN, Priyanka K, Prasad S, Singh S, Kim JM (2013) A class of estimators for population variance in two occasion rotation patterns. Commun Stat Appl Methods 20(4):247–257Google Scholar
  12. 12.
    Rubin DB (1976) Inference and missing data. Biometrika 63(3):581–592MathSciNetCrossRefGoogle Scholar
  13. 13.
    Sande IG (1979) A personal view of hot-deck imputation procedures. Surv Methodol 5:238–247Google Scholar
  14. 14.
    Lee H, Rancourt E, Sarndall CE (1994) Experiments with variance estimation from survey data with imputed values. J Off Stat 10(3):231–243Google Scholar
  15. 15.
    Heitzan DF, Basu S (1996) Distinguish ‘missing at random’ and ‘missing completely at random. Am Stat 50:207–217Google Scholar
  16. 16.
    Singh S (2009) A new method of imputation in survey sampling. Statistics 43(5):499–511MathSciNetCrossRefGoogle Scholar
  17. 17.
    Diana G, Perri PF (2010) Improved estimators of the population mean for missing data. Commun Stat Theory Methods 39:3245–3251MathSciNetCrossRefGoogle Scholar
  18. 18.
    Singh S, Joarder AH, Tracy DS (2000) Regression type estimators of random non-response in survey sampling. Statistica LX, 1:39–44MathSciNetzbMATHGoogle Scholar
  19. 19.
    Agrawal MC, Roy DC (1999) Efficient estimators of population variance with regression-type and ratio-type predictor-inputs. Metron LVII(3):169–178MathSciNetzbMATHGoogle Scholar
  20. 20.
    Sukhatme PV, Sukhatme BV (1970) Sampling theory of surveys with applications. Asia Publishing House, New DelhizbMATHGoogle Scholar
  21. 21.
    Murthy MN (1967) Sampling theory and methods. Statistical Publishing Society, CalcuttazbMATHGoogle Scholar
  22. 22.
    Ministry of Statistics & Programme Implementation (2013) Chapter-2(2.1).

Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  1. 1.Department of MathematicsNIT- RaipurRaipurIndia
  2. 2.Department of Statistics, Sri Venkateswara CollegeUniversity of DelhiNew DelhiIndia

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