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Optimal Strategy for Elevated Estimation of Population Mean in Stratified Random Sampling under Linear Cost Function

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Abstract

In this paper, we propose the exponential ratio-type estimator for the elevated estimation of population mean, implying one auxiliary variable in stratified random sampling using the conventional ratio and, Bahl and Tuteja exponential ratio-type estimators. The bias and the Mean Squared Error (MSE) of the proposed estimator are derived up to a first-order approximation and compared with existing estimators. Theoretically, we also compare MSE of the proposed estimator using the linear cost function with the competing estimators. The optimal values of the characterizing scalars are obtained and for these optimal values of characterizing scalars, the minimum MSE is obtained. We find theoretically that the proposed estimator is more efficient than other estimators under restricted conditions by formulating the proposed problem as an optimization problem under linear cost function. The numerical illustration is also included to verify theoretical findings for their practical utility. The estimator with least MSE is recommended for practical utility in different areas of applications of stratified random sampling.

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References

  1. Cochran WG (1940) The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. J Agric Sci 30(2):262–275. https://doi.org/10.1017/S0021859600048012

    Article  Google Scholar 

  2. Sisodia BVS, Dwivedi VK (1981) A class of ratio-cum-product-type estimator. Biom J 23(2):133–139. https://doi.org/10.1002/bimj.4710230204

    Article  Google Scholar 

  3. Bahl S, Tuteja RK (1991) Ratio and product type exponential estimators. J Inf Optim Sci 12(1):159–163. https://doi.org/10.1080/02522667.1991.10699058

    Article  Google Scholar 

  4. Upadhyaya LN, Singh HP (1999) Use of transformed auxiliary variable in estimating the finite population mean. Biom J 41(5):627–636. https://doi.org/10.1002/(SICI)1521-4036(199909)41:5%3c627::AID-BIMJ627%3e3.0.CO;2-W

    Article  Google Scholar 

  5. Singh HP, Tailor R (2003) Use of known correlation coefficient in estimating the finite population mean. Stat Trans 6:553–560

    Google Scholar 

  6. Kadilar C, Cingi H (2003) Ratio estimators in simple random sampling. Appl Math Comput 151:893–902. https://doi.org/10.1016/S0096-3003(03)00803-8

    Article  Google Scholar 

  7. Yadav SK, Kadilar C (2013) Improved class of ratio and product estimators. Appl Math Comput 219:10726–10731. https://doi.org/10.1016/j.amc.2013.04.048

    Article  Google Scholar 

  8. Singh HP, Vishwakarma GK (2008) A family of estimators of population mean using auxiliary information in stratified sampling. Comm Statist Theory Methods 37:1038–1050. https://doi.org/10.1080/03610920701713237

    Article  Google Scholar 

  9. Jerajuddin M, Kishun J (2016) Modified ratio estimators for population mean using size of the sample selected from population. Int J Sci Res Sci Eng Technol 2:10–16

    Google Scholar 

  10. Shabbir J, Gupta S (2005) Improved ratio estimators in stratified sampling. Am J Math Manag Sci 25(3–4):293–311

    Google Scholar 

  11. Koyuncu N, Kadilar C (2009) Ratio and product estimators in stratified random sampling. J Statist Plann Inference 139(8):2552–2558

    Article  Google Scholar 

  12. Tailor R, Sharma B (2009) A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis. Stat Trans 10(1):15–24

    Google Scholar 

  13. Koyuncu N, Kadilar C (2010) On improvement in estimating population mean in stratified random sampling. J Appl Stat 37(6):999–1013

    Article  Google Scholar 

  14. Singh HP, Vishwakarma GK (2010) A general procedure for estimating the population mean in stratified sampling using auxiliary information. Metron 68(1):47–65

    Article  Google Scholar 

  15. Tailor R, Sharma B, Kim JM (2011) A generalized ratio-cum-product estimator of finite population mean in stratified random sampling. Commun Korean Stat Soc 18(1):111–118

    Google Scholar 

  16. Solanki RS, Singh HP (2015) Efficient classes of estimators in stratified random sampling. Statist Papers 56(1):83–103

    Article  Google Scholar 

  17. Singh R, Kumar M, Singh RD, Chaudhry MK (2013). Exponential ratio type estimators in stratified random sampling, https://doi.org/10.48550/ar**v.1301.5086

  18. Singh R, Kumar M, Chaudhary MK, Kadilar C (2009) Improved exponential estimator in stratified random sampling. Pak J Stat Oper Res 5(2):67–82

    Article  Google Scholar 

  19. Shabbir J, Gupta S (2011) On estimating finite population mean in simple and stratified random sampling. Comm Statist Theory Methods 40:199–212

    Article  Google Scholar 

  20. Haq A, Shabbir J, Gupta S (2013) Improved exponential ratio type estimators in stratified sampling. Pakistan J Stat 29(1):13–31

    Google Scholar 

  21. Tailor R, Chouhan S, Tailor R, Garg N (2012) A ratio-cum-product estimator of population mean in stratified random sampling using two auxiliary variables. Statistica (Bologna) 72(3):287–297

    Google Scholar 

  22. Subramani J, Kumarapandiyan G (2012) Estimation of population mean using coefficient of variation and median of an auxiliary variable. Int J Probab Stat 1(4):111–118

    Google Scholar 

  23. Yadav SK, Mishra SS (2015) Develo** improved predictive estimator for finite population mean using auxiliary information. Statistika-Stat Econom J 95(1):76–85

    Google Scholar 

  24. Yadav SK, Sharma DK, Mishra SS, Shukla AK (2018) Use of auxiliary variables in searching efficient estimator of population mean. Int J Multivar Data Anal 1(3):230–244

    Article  Google Scholar 

  25. Yadav SK, Mishra SS, Gupta S (2019) An efficient estimator for population variance using parameters of an auxiliary variable. J Stat Manag Syst 22(6):1005–1013

    Google Scholar 

  26. Singh N, Vishwakarma GK, Kim JM (2022) Computing the effect of measurement errors on efficient variant of the product and ratio estimators of mean using auxiliary information. Comm Statist Simulation Comput 51(2):604–625

    Article  Google Scholar 

  27. Tschuprow AA (1923) On the mathematical exception of the moments of frequency distribution in the case of correlated observations. Metron 2:461–493

    Google Scholar 

  28. Neyman J (1934) On the two different aspect of representative method: the method of stratified sampling and method of purposive selection. J R Stat Soc 97(4):558–625. https://doi.org/10.2307/2342192

    Article  Google Scholar 

  29. Yates F (1960) Sampling methods for censuses and surveys. Charles Griffin and Co Ltd, London

    Google Scholar 

  30. Chatterjee S (1967) A note on optimum allocation. Scand Actuar J 50:40–44

    Article  Google Scholar 

  31. Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York

    Google Scholar 

  32. Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, Berlin

    Book  Google Scholar 

  33. Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178

    Article  Google Scholar 

  34. Mradula, Yadav SK, Varshney R, Dube M (2021) Efficient estimation of population mean under stratified random sampling with linear cost function. Comm Statist Simulation Comput 50(12):4364–4387. https://doi.org/10.1080/03610918.2019.164347

    Article  Google Scholar 

  35. Shabbir J, Ahmed A (2022) Estimation of interquartile range in stratified sampling under non-linear cost function. Comm Statist Simulation Comput 51(4):1891–1898

    Article  Google Scholar 

  36. Aggarwal S, Soni SS, Chaubey RS (2022) Estimation of the population mean by develo** a new estimator. Bull Pure Appl Sci Sect E Math Stat 41(1):11–15

    Google Scholar 

  37. Shi Y (2022) Advances in Big Data Analytics: Theory, Algorithm and Practice, Springer, Singapore.

  38. Gupta S, Haq A, Varshney R (2022) Problem of compromise allocation in multivariate stratified sampling using intuitionistic fuzzy programming. Ann Data Sci. https://doi.org/10.1007/s40745-022-00410-y

    Article  Google Scholar 

  39. Murthy MN (1967) Sampling theory and methods. Statistical Publishing Society, Calcutta

    Google Scholar 

  40. Khan MGM, Khan EA, Ahsan MJ (2008) Optimum allocation in multivariate stratified sampling in presence of non-response. J Indian Soc Agri Statist 62(1):42–48

    Google Scholar 

  41. Lasdon LS (1970) Optimization theory for large systems. MacMillan, New York

    Google Scholar 

Download references

Acknowledgements

The authors are very much thankful to the editor and the learned referees for their valuable comments, which improved the manuscript.

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Authors and Affiliations

  1. Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India

    Subhash Kumar Yadav, Mukesh Kumar Verma & Rahul Varshney

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  1. Subhash Kumar Yadav
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  3. Rahul Varshney
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All the authors contributed equally to this work.

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Correspondence to Rahul Varshney.

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Appendix 1

Appendix 1

See Tables 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

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Yadav, S.K., Kumar Verma, M. & Varshney, R. Optimal Strategy for Elevated Estimation of Population Mean in Stratified Random Sampling under Linear Cost Function. Ann. Data. Sci. (2024). https://doi.org/10.1007/s40745-024-00520-9

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