Skip to main content
SpringerLink
Log in

Estimation of Population Parameters Using the Technique of Sub-sampling from Non-respondents in Sample Surveys: A Review

  • Review
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

While conducting a mail survey to reduce the cost, the rate of non-response becomes high which leads to non-response in the units selected in the sample which lacks the representative of the population parameters based on the values of the characteristics for respondents as well as non-respondents in the population. In the case of non-response on the units selected in the sample, the estimators of the population parameters suffer from bias due to non-response and from the loss in the efficiency of the estimator. The present research work is an attempt to review the research work done in the area of estimation of several parameters of the population such as population mean, ratio and product of two population mean etc. using auxiliary information in the presence of non-response in the direction of Hansen and Hurwitz’s technique using the method of sub-sampling from non-respondents. Various methods proposed by several authors for the estimation of population parameters using auxiliary character in the presence of non-response in different situations have been discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Khare BB (1994) A brief glance at the methods for eradicating the effect of non-response. SRG Bull India 1:53–61

    Google Scholar 

  2. Hansen MH, Hurwitz WN (1946) The problem of non-response in sample surveys. J Amer Stat Assoc 41:517–629

    Article  Google Scholar 

  3. E-Badry MA (1956) A sampling proced-ure for mailed questionnaires. J Amer Stat Assoc 51:209–227

    Article  Google Scholar 

  4. Foradori GT (1961) Some non-response sam-pling theory for two stage designs, North Carolina State College. Mimeograped Series, No. 297 Raleigh

  5. Srinath KP (1971) Multiphase sampling in non- response problems. J Amer Stat Assoc 66:583–586

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  7. Khare BB (2003) Use of auxiliary information in sample survey up to 2000- A review. In: Sen DK, Mishra PK (eds) Mathematics and statistics in engineering, biotechnology and science. M/S Centre for Bio-Mathematical Studies, India, pp 76–87

    Google Scholar 

  8. Cochran WG (1977) Sampling techniques, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  9. Rao PSRS (1986) Ratio estimation with sub-sampling the non-respondents. Survey Methodol 12:217–230

    Google Scholar 

  10. Rao PSRS (1987) Ratio and regression Estimates with Sub-sampling the non-respondents. Paper presented at a special contributed session of the International Statistical Association Meetings, September, 2–16, 1987, Tokyo, Japan

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

    Google Scholar 

  12. Khare BB (2003) A comparative study of ratio, product and regression type estimators for population mean in presence of non-response. In: Sen DK, Mishra PK (eds) Mathematics and statistics in engineering, biotechnology and science. M/S Centre for Bio-Mathematical Studies, India, pp 217–226

    Google Scholar 

  13. Khare BB, Srivastava S (1993) Estimation of population mean using auxiliary character in presence of nonresponse. Natl Acad Sci Letter 16:111–114

    MATH  Google Scholar 

  14. 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 65:195–203

    MATH  Google Scholar 

  15. Khare BB, Srivastava S (1999) Conventional and alternative two phase sampling regression type estimators for population mean in presence of nonresponse. In: Chattopadhyay A (ed) Recent trend and advances of Mathematics and Statistics in Engineering and Technology. Narosa Publishing House, London pp, pp 97–101

    Google Scholar 

  16. Khare BB, Srivastava S (1999–2000) A study of two phase sampling product type estimators for population mean in presence of non response under super population model approach. Proc Math Soc BHU 15–16: 69–75

  17. Khare BB, Srivastava S (2002) Study of two phase sampling ratio type estimators for population mean in presence of non-response under super population model approach. Proc Natl Acad Sci India 72:331–337

    MATH  MathSciNet  Google Scholar 

  18. Srivastava SK (1967) An estimator using auxiliary information in sample surveys. Cal Stat Assoc Bull 16:121–132

    Google Scholar 

  19. Khare BB, Srivastava S (2000) Generalised estimator for population mean in presence of non-response. Intern J Math Stat Sci (Brazil) 9:75–87

    MATH  MathSciNet  Google Scholar 

  20. Khare BB, Srivastava S (1996) Transformed product type estimators for population mean in presence of softcore observations. Proc Math Soc BHU 12:29–34

    Google Scholar 

  21. Khare BB, Srivastava S (1997) Transformed ratio type estimators for the population mean in the presence of nonresponse. Commun Stat-Theory Methods (USA) 26:1779–1791

    Article  MATH  MathSciNet  Google Scholar 

  22. Khare (2002) A class of estimators for populations mean using auxiliary character in presence of soft core observations. Prog Math 36:1–9

    MATH  MathSciNet  Google Scholar 

  23. Singh HP, Kumar S (2009) A general class of estimators of the population mean in survey sampling using auxiliary information with sub sampling the non-respondents. Korean J Appl Stat 22:387–402

    Article  Google Scholar 

  24. Singh HP, Kumar S (2008) A regression approach to the estimation of the finite population mean in the presence of non- response. Aust N Z J Stat 50:395–408

    Article  MathSciNet  Google Scholar 

  25. Khare BB, Kumar S (2009) Transformed two phase sampling ratio and product type estimators for population mean in the presence of non-response. Aligarh J Stat 29:91–106

    MathSciNet  Google Scholar 

  26. Singh HP, Ruiz Espejo M (2007) Double sampling ratio-product estimator of a finite population mean in sample survey. J Appl Stat 34:71–85

    Article  MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  28. Khare BB, Sinha, RR (2002) General class of two phase sampling estimators for population mean using and auxiliary character in presence of non response. Proc. of Vth international symposium on optimization and Statistics held at AMU Aligarah 233–245

  29. Khare BB, Kumar A, Sinha R, Pandey SK (2008) Two phase sampling estimators for population mean using auxiliary character in presence of non-response. J Sci Res 52:271–281

    Google Scholar 

  30. Khare BB, Pandey SK, Srivastava U (2011) An improved class of two phase sampling estimator for population mean using auxiliary character in the presence of non response. J Sci Res BHU 55:151–161

    Google Scholar 

  31. Singh HP, Kumar S (2010) Estimation of mean in presence of non-response using two phase sampling scheme. Stat Pap 51:559–582

    Article  MATH  MathSciNet  Google Scholar 

  32. Khare BB, Srivastava U, Kumar K (2012) An improved class of estimators for population mean using auxiliary character in the presence of non-response. Natl Acad Sci Lett 35:361–366

    Article  Google Scholar 

  33. Singh HP, Kumar S (2009) A general procedure of estimating the population mean in the presence of non-response under double sampling using auxiliary information. SORT-Stat Oper Res 33:71–83

    MATH  MathSciNet  Google Scholar 

  34. Ismail M, Shahbaz QS, Hanif M (2011) A general class of population mean in presence of non-response. Pak J Stat 27:467–476

    MathSciNet  Google Scholar 

  35. Kumar S, Singh HP, Bhougal S (2011) A class of ratio-cum-product type estimators under double sampling in the presence of non-response. Hacettepe J Mathe Statistics 40:589–599

    MATH  MathSciNet  Google Scholar 

  36. Singh HP, Kumar S, Kozak M (2010) Improved estimation of finite population mean when sub-sampling is employed to deal with non-response. Commun Stats-Theory-Methods 39:791–802

    Article  MATH  MathSciNet  Google Scholar 

  37. Singh HP, Kumar S (2010) Improved estimation of population mean under two-phase sampling with subsampling the non-respondents. J Stat Plan Inference 140:2536–2550

    Article  MATH  MathSciNet  Google Scholar 

  38. Khare BB, Kumar S (2010) Chain regression type estimators using additional auxiliary variable in two phase sampling in the presence of non-response. Natl Acad Sci Lett India 33:369–375

    Google Scholar 

  39. Khare BB, Srivastava U, Kumar K (2011) Generalized chain estimators for the population mean in the presence of non response. Proc Nat Acad Sci India 81:231–238

    MathSciNet  Google Scholar 

  40. Singh HP, Kumar S (2011) Combination of regression and ratio estimate in presence of non-response. Brazilian J Probab Stat 25:205–217

    Article  MathSciNet  Google Scholar 

  41. Khare BB, Kumar S (2009) Utilization of coefficient of variation in the estimation of population mean using auxiliary character in the presence of non-response. Natl Acad Sci Lett India 32:235–241

    Google Scholar 

  42. Khare BB, Kumar S (2011) Estimation of population mean using known coefficient of variation of the study character in the presence of non response. Commun Stat-Theory Methods 40:1–15

    Article  MathSciNet  Google Scholar 

  43. Khare BB, Sinha RR (2009) On class of estimator for population mean using multi-auxiliary character in presence of non-response. Stat Transition-new series (Poland) 10:3–14

    Google Scholar 

  44. Khare BB, Sinha RR (2011) Estimation of population of population mean using multi-auxiliary characters with sub sampling the nonrespondents. Stat Transition-new series 12:45–56

    Google Scholar 

  45. Kumar S, Singh HP (2010) Estimation of mean using multi-auxiliary informations in presence of non-response. Commun Korean Stat Soc 17:3391–3411

    Article  MathSciNet  Google Scholar 

  46. Khare BB (1987) Allocation in stratified sampling in presence on non-response. Metron (Italy) 45(I/II):213–221

    MathSciNet  Google Scholar 

  47. Sodipo AA (1998) A ratio-type estim-ation for the population mean with subsampling and post-stratification of the nonrespondents. J Niger Stat 1:44–53

    Google Scholar 

  48. Shukla D, Dubey J (2001) Estimation in mail surveys under PSNR sampling scheme. J Ind Soc Agric Stat 54:288–302

    MathSciNet  Google Scholar 

  49. Shukla D, Dubey J (2004) On estimation under post stratified two phase non-response sampling scheme in mail surveys. Int J Manag Syst 20:269–278

    Google Scholar 

  50. Shukla D, Dubey J (2007) On PSNR sampling scheme for mean estimation. Statistics In Transition-ns 8:71–87

    Google Scholar 

  51. Khare BB, Pandey SK (2008) Separate generalized two phase sampling estimator for population mean with post stratification in presence of non-response. J Stat Stud 27:5–15

    MathSciNet  Google Scholar 

  52. Sodipo AA (2010) A generalized class ratio-type estimator of population mean based on poststratification and subsampling of the nonrespondents. Eur J Sci Res 42:662–667

    Google Scholar 

  53. Sodipo AA (2010) Difference -type and regression-type estimators for the population mean based on post-stratification and subsampling of the nonrespondents. Eur J Sci Res 43:445–451

    Google Scholar 

  54. Tripathi TP, Khare BB (1997) Estimation of mean vector in presence of non-response. Commun Statist—Theory Meth (USA) 26:2255–2269

    Article  MATH  MathSciNet  Google Scholar 

  55. Khare BB, Pandey SK (2000) A class of estimators for ratio of two population means using auxiliary character in presence of non-response. J Sci Res BHU 50:115–124

    Google Scholar 

  56. Khare BB, Sinha RR (2010) On class of estimators for the product of two population means using auxiliary character in presence of non-response. Inter Trans Appl Sci 2:841–846

    Google Scholar 

  57. Khare BB, Sinha RR (2002) Estimation of the ratio of two populations means using auxiliary character with unknown population mean in presence of nonresponse. Prog Maths 36:337–348

    MATH  MathSciNet  Google Scholar 

  58. Khare BB, Sinha RR (2004) Estimation of finite population ratio using two phase sampling in presence of no response. Aligarh J Stat 24:43–56

    MathSciNet  Google Scholar 

  59. Khare BB, Srivastava U, Kumar K (2012) Chain type estimators for ratio of two population means using auxiliary characters in the presence of non-response. J Sci Res BHU 56:183–196

    Google Scholar 

  60. Khare BB, Sinha RR (2012) Combined class of estimators for ratio and product of two population means in presence of non-response. Int J Stat Econ 8:86–95

    MathSciNet  Google Scholar 

  61. Khare BB, Srivastava U, Kumar K (2013) Generalized chain estimators for ratio of two population means using two auxiliary characters in the presence of non-response. Int J Stat Econ 10:51–64

    MathSciNet  Google Scholar 

  62. Khare BB, Sinha RR (2007) Estimation of the ratio of the two population means using multi- auxiliary characters in presence of non-response. In “Statistical techniques in life testing, reliability, sampling theory and quality control” edited by B N Pandey. Narosa publishing house New Delhi 163–171

  63. Khare BB, Sinha RR (2012) Improved classes of estimators for ratio of two means with double sampling the nonrespondents. Statistika 49:75–83

    Google Scholar 

  64. Khare BB, Sinha RR (2002) On class of two phase sampling estimators for the product of two population means using auxiliary character in presence of non response. Proc. of Vth international symposium on optimization and Statistics held at AMU Aligarh 221–232

  65. Khare BB, Sinha RR (2004) On the general class of two phase sampling estimators for the product of two population means using the auxiliary characters in the presence of non-response. Ind J Appl Stat 8:1–14

    Google Scholar 

  66. Singh HP, Kumar S (2010) A general class of DSS estimators of population ratio, product and mean in the presence of non-response based on the sub-sampling of the non-respondents. Pak J Stats 26:203–238

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Banaras Hindu University, Varanasi, 221005, India

    B. B. Khare

Authors
  1. B. B. Khare
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. B. Khare.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khare, B.B. Estimation of Population Parameters Using the Technique of Sub-sampling from Non-respondents in Sample Surveys: A Review. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 84, 337–343 (2014). https://doi.org/10.1007/s40010-013-0107-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-013-0107-3

Keywords

Search

Navigation