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Optimal Random Non Response Frameworks for Mean Estimation on Current Occasion

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Abstract

In this paper, we propose various sampling strategies under random non response framework and proposed estimators to estimate population mean on current occasion. The formulation of the estimator is allied with Cochran (1977) and Searls (J. Am. Stat. Assoc. 59, 1225–1226 1964) in the framework of random non response. The characteristics of each proposed estimator have been studied under optimum replacement policy. We have examined the performance of these estimators under the analytical study and validated it through numerical study. We have also gauged the loss with the available complete response case and reported in numerical illustration. Suitable recommendations have been put forward to the survey statisticians for its practical application.

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References

  • Ahmed, M.S., Al-Titi, O., Al-Rawib, Z. and Abu-Dayyeh, W. (2005). Estimation of finite population variance in presence of random non-response using auxiliary variables. Inf. Manag. Sci. 16, 73–82.

    MathSciNet  Google Scholar 

  • Bandyopadhyay, A. and Singh, G.N. (2014). On the use of two auxiliary variables to improve the precision of estimate in two-occasion successive sampling. Int. J. Math. Stat. 15, 73–88.

    MathSciNet  Google Scholar 

  • Bartholomew, D.J. (1961). A method of allowing for ‘not-at-home’ bias in sample surveys. J. R. Stat. Soc. Series C (Appl. Stat.) 10, 52–9.

  • Bhushan, S. and Pandey, S. (2020). A cost-effective computational approach with non response on two occasions. Commun. Stat. - Theory Methods 49, 4951–4973.

    Article  MathSciNet  Google Scholar 

  • Biradar, R.S. and Singh, H.P. (2001). Successive sampling using auxiliary information on both occasions. Calcutta Stat. Assoc. Bull. 51, 243–251.

    Article  MathSciNet  Google Scholar 

  • Chatterjee, A., Singh, G.N. and Bandyopadhyay, A. (2019). Estimation of population mean in successive sampling under super-population model in presence of random non response situations. Commun. Stat. - Theory Methods 48, 3850–3863.

    Article  MathSciNet  Google Scholar 

  • Chaturvedi, D.K. and Tripathi, T.P. (1983). Estimation of population ratio on two occasions using multivariate auxiliary information. J. Indian Statistical Association 21, 11320.

    MathSciNet  Google Scholar 

  • Choudhary, R.K., Bathla, H.V.L. and Sud, U.C. (2004). On non-response in sampling on two occasions. J. Ind. Soc. Ag. Statistics 58, 331–43.

    MathSciNet  Google Scholar 

  • Cochran W.G. (1977). Sampling Techniques, 3rd edition. Wiley Eastern Limited.

  • Das, A.K. (1982). Estimation of population ratio on two occasions. J. Ind. Soc. Ag. Statistics 34, 1–9.

    Google Scholar 

  • Eckler, A.R. (1955). Rotation sampling. Ann. Math. Stat. 664–685.

  • Feng, S. and Zou, G. (1997). Sample rotation method with auxiliary variable. Commun. Stat. - Theory Methods 26, 1497–509.

    Article  MathSciNet  Google Scholar 

  • Gupta, P.C. (1979). Sampling on two successive occasions. J. Stat. Res. 13, 7–16.

    MathSciNet  Google Scholar 

  • Hansen, M.H. and Hurwitz, W.N. (1946). The problem of the nonresponse in sample surveys. J. Amer. Statist. Assoc. 41, 517–529.

    Article  Google Scholar 

  • Heitjan, D.F. and Basu, S. (1996). Distinguishing “missing at random” and “missing completely at random”. Am. Stat. 50, 207–213.

  • Jessen, R.J. (1942). Statistical Investigation of a Sample Survey for obtaining farm facts. Iowa Agricultural Experiment Station Research, Bulletin No. 304, Ames, Iowa, U. S. A., 1–104.

  • Okafor, F.C. (2001). Treatment of nonresponse in successive sampling. Statistica 51, 195–204.

  • Patterson, H.D. (1950). Sampling on successive occasions with partial replacement of units. J. R. Stat. Soc. B12, 241–255.

    Google Scholar 

  • Ralte, Z. and Das, G. (2015). Ratio-to-regression estimator in successive sampling using one auxiliary variable. Stat. Transit. new series 2, 183–202.

    Article  Google Scholar 

  • Rao, J.N.K. and Graham, J.E. (1964). Rotation designs for sampling on repeated occasions. J. Am. Stat. Assoc. 59, 492–509.

    Article  MathSciNet  Google Scholar 

  • Rubin, D.B. (1976). Inference and missing data. Biometrika 63, 581–592.

    Article  MathSciNet  Google Scholar 

  • Searls, D.T. (1964). Utilization of known coefficients of Kurtosis in the estimation procedure of variance. J. Am. Stat. Assoc. 59, 1225–1226.

    Article  Google Scholar 

  • Singh, S. (2003). Advanced Sampling Theory with Applications. Kluwer Academics Press.

  • Singh, H.P. and Vishwakarma, G.K. (2007). A general class of estimators in successive sampling. Metron LXV 201227.

  • Singh, G.N. (2005). On the use of chain-type ratio estimator in successive sampling. Stat. Transit. 7, 21–26.

    Google Scholar 

  • Singh, H.P. and Joarder, A.H. (1998). Estimation of finite population variance using random non-response in sample surveys. Metrica 47, 241–249.

    Article  Google Scholar 

  • Singh, G.N. and Karna, J.P. (2009). Estimation of population mean on current occasion in two-occasion successive sampling. Metron 67, 69–85.

    Google Scholar 

  • Singh, G.N. and Prasad, S. (2013). Best linear unbiased estimators of population mean on current occasion in two-occasion successive sampling. Statistics in Transition-New Series 14, 57–74.

    Article  Google Scholar 

  • Singh, G.N. and Priyanka, K. (2008). Use of super-population model in search of good rotation patterns on successive occasions. J. Stat. Res. 42, 127–41.

    MathSciNet  Google Scholar 

  • Singh, G.N. and Sharma, A.K. (2016). Estimation of population mean on current occasion using multiple auxiliary information in h-occasion successive sampling. J. Stat. Appl. Probab. Lett. 3, 19–27.

    Google Scholar 

  • Singh, G.N. and Singh, V.K. (2001). On the use of auxiliary information in successive sampling. J. Ind. Soc. Ag. Statistics 54, 112.

    MathSciNet  Google Scholar 

  • Singh, H.P. and Tracy, D.S. (2001). Estimation of population mean in presense of random non-response in sample surveys. Statistica 61, 231–248.

    MathSciNet  Google Scholar 

  • Singh, H.P. and Vishwakarma, G.K. (2009). A general procedure for estimating population mean in successive sampling. Commun. Stat. - Theory Methods 38, 293308.

  • Singh, D., Singh, R. and Singh, P. (1974). Study of nonresponse in successive sampling. J. Ind. Soc. Ag. Statistics 26, 37–41.

    Google Scholar 

  • Singh V.K., Singh, G.N. and Shukla, D. (1991). An efficient family of ratio cum difference type estimators in successive sampling over two occasions. J. Sci. Res. 41, 149–159.

    Google Scholar 

  • Singh, H.P., Chandra, P., Joarder, A.H. and Singh, S. (2007). Family of estimators of mean, ratio and product of a finite population using random non-response. TEST 16, 565–597.

    Article  MathSciNet  Google Scholar 

  • Singh, H.P., Tailor, R., Kim, J.M. and Singh, S. (2012). Families of estimators of finite population variance using a random non-response in survey sampling. Korean J. Appl. Atat. 25, 681–695.

    Article  Google Scholar 

  • Singh G.N., Sharma A.K. and Bandyopadhyay A. (2016). Effectual variance estimation strategy in two occasions successive sampling in presence of random non-response. Commun. Stat. - Theory Methods.

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Author information

Authors and Affiliations

  1. Deapartment of Statistics, University of Lucknow, Lucknow, Uttar Pradesh, India

    Shashi Bhushan

  2. Deapartment of Management, Galgotias University, Greater Noida, Uttar Pradesh, India

    Shailja Pandey

Authors
  1. Shashi Bhushan
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  2. Shailja Pandey
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Correspondence to Shailja Pandey.

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Appendix

Appendix

Table 11 PRE and loss under the proposed strategy I
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Table 12 PRE and loss under the proposed strategy I for \(p_1=0.10\) and \(\rho _{yx}=0.8038\)
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Table 13 PRE and loss under the proposed strategy I for \(p_1=0.15\) and \(\rho _{yx}=0.8038\)
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Table 14 PRE and loss under the proposed strategy I for \(p_1=0.20\) and \(\rho _{yx}=0.8038\)
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Table 15 PRE and loss under the proposed strategy I for \(p_1=0.05\) and \(\rho _{yx}=0.5\)
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Table 16 PRE and loss under the proposed strategy I for \(p_1=0.10\) and \(\rho _{yx}=0.5\)
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Table 17 PRE and Loss under the proposed strategy I for \(p_1=0.15\) and \(\rho _{yx}=0.5\)
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Table 18 Loss and PRE under the proposed strategy I for \(p_1=0.20\) and \(\rho _{yx}=0.5\)
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Table 19 PRE and loss under the proposed strategy I for \(p_1=0.05\) and \(\rho _{yx}=0.6\)
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Table 20 PRE and loss under the proposed strategy I for \(p_1=0.10\) and \(\rho _{yx}=0.6\)
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Table 21 PRE and loss under the proposed strategy I for \(p_1=0.15\) and \(\rho _{yx}=0.6\)
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Table 22 Loss and PRE under the proposed strategy I for \(p_1=0.20\) and \(\rho _{yx}=0.6\)
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Table 23 PRE and loss under the proposed strategy I for \(p_1=0.05\) and \(\rho _{yx}=0.7\)
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Table 24 Loss and PRE under the proposed strategy I for \(p_1=0.10\),= and \(\rho _{yx}=0.7\)
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Table 25 PRE and loss under the proposed strategy I for \(p_1=0.15\) and \(\rho _{yx}=0.7\)
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Table 26 Loss and PRE under the proposed strategy I for \(p_1=0.20\) and \(\rho _{yx}=0.7\)
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Table 27 PRE and loss under the proposed strategy I for \(p_1=0.05\) and \(\rho _{yx}=0.9\)
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Table 28 Loss and PRE under the proposed strategy I for \(p_1=0.10\) and \(\rho _{yx}=0.9\)
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Table 29 PRE and loss under the proposed strategy I for \(p_1=0.15\), \(\rho _{yx}=0.9\)
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Table 30 Loss and PRE under the proposed strategy I for \(p_1=0.20\) and \(\rho _{yx}=0.9\)
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Table 31 PRE and loss under the proposed strategy II for \(\rho _{yx}=0.5\)
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Table 32 PRE and loss under the proposed strategy II for \(\rho _{yx}=0.6\)
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Table 33 PRE and loss under the proposed strategy II for \(\rho _{yx}=0.7\)
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Table 34 PRE and loss under the proposed strategy II for \(\rho _{yx}=0.9\)
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Table 35 PRE and Loss under the proposed strategy III for \(\rho _{yx}=0.5\)
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Table 36 PRE and loss under the proposed strategy III for \(\rho _{yx}=0.6\)
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Table 37 PRE and loss under the proposed strategy III for \(\rho _{yx}=0.7\)
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Table 38 PRE and loss under the proposed strategy III for \(\rho _{yx}=0.9\)
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Table 39 PRE and loss under the proposed strategy IV for \(\rho _{yx}=0.5\)
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Table 40 PRE and loss under the proposed strategy IV for \(\rho _{yx}=0.6\)
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Table 41 PRE and loss under the proposed strategy IV for \(\rho _{yx}=0.7\)
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Table 42 PRE and loss under the proposed strategy IV for \(\rho _{yx}=0.9\)
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Bhushan, S., Pandey, S. Optimal Random Non Response Frameworks for Mean Estimation on Current Occasion. Sankhya B (2024). https://doi.org/10.1007/s13571-024-00330-2

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