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Calibrated Estimators for Population Means Using Standard Deviation of the Auxiliary Variable

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Abstract

In this paper, a new calibration constraint, using known standard deviation of the auxiliary variable was proposed for obtaining calibration estimators for the population means. Also, the condition for assessing the efficiency of the proposed estimators with the existing estimators was derived. The proposed estimators were compared with existing estimators using the biases and mean square errors based empirical and simulation studies. The results of the empirical study showed that the mean square errors of the proposed estimators were less than the existing estimators indicating that the proposed estimators are more efficient compared to the existing estimators considered in this study. Also, from the simulation study, the results showed that increase in the sample size, increases the performance of the proposed estimators over the existing estimators.

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References

  • Adubi SA, Babatunde OT, Ude OI (2022) Modified ratio estimators for population means with two auxiliary parameters using calibration weights. Asian J Prob Stat 20(4):169–183

    Google Scholar 

  • Alam S, Shabbir J (2020) Calibration estimation of mean by using double use of auxiliary information. Commun Stat Simu Comput. https://doi.org/10.1080/03610918.2020.1749660

    Article  MATH  Google Scholar 

  • Alam S, Singh S, Shabbir J (2019. New methodology of calibration in stratified random sampling. Surv Res Methods Section, 90–95. https://doi.org/10.1080/00949655.2019.1688813

  • Alam S, Singh S, Shabbir J (2020) Calibrated estimators using non-linear calibration constraints. J Stat Comput Simul 90(3):489–514

    Article  MathSciNet  MATH  Google Scholar 

  • Ashok KJ, Mahamood U, Garib NS (2023). New calibration estimation procedure in the presence of unit non response. Ain Shams Eng J 14(3). https://doi.org/10.1016/j.asej.2022.101910

  • Audu A, Singh R, Khare S (2021) Developing calibration estimators for population mean using robust measures of dispersion under stratified random sampling. Stat Trans 22(2):125–142

    Google Scholar 

  • Babatunde OT, Oladugba AV, Ude IO, Adubi AS (2023) Calibration estimation of population mean in stratified sampling using standard deviation. Qual Quant. https://doi.org/10.1007/s11135-023-017371

    Article  Google Scholar 

  • Clement EP (2015) Improving the efficiency of ratio estimators by calibration weightings. Nigerian Stast Assoc Proc (September 2015), pp 481–493

  • Clement EP (2020) On the estimation of variance of calibration regression estimators with multiple auxiliary information. Asian J Prob Stat 10(1):25–35

    Article  Google Scholar 

  • Clement EP, Enang EI (2015) Calibration approach alternative ratio estimator for population mean in stratified sampling. Int J Stat Econ, pp 83–93

  • Deville JC, Särndal CE (1992) Calibration estimators in survey sampling. J Am Stat Assoc 87(418):376–382

    Article  MathSciNet  MATH  Google Scholar 

  • Enang EI, Clement EP (2019) An efficient class of calibration ratio estimators of domain mean in survey sampling. Commun Math Stat. https://doi.org/10.1007/s40304-018-00174-z

    Article  MATH  Google Scholar 

  • Eyo EE, Enang IE (2022) Calibration ratio estimators of population mean using median of auxiliary variable. J Model Simul Mater 5(1):21–30

    Article  Google Scholar 

  • Farrell PJ, Singh S (2005) Model-assisted higher order calibration of estimators of variance. Aust N Z J Stat 47(3):375–383

    Article  MathSciNet  MATH  Google Scholar 

  • Garg N, Pachori M (2019) Use of median in calibration estimation of the finite population mean in stratified sampling. Int J Comput Sci Eng 7(5):667–671

    Google Scholar 

  • Iseh MJ, Bassey KJ (2021) Calibration estimator for population mean in small sample size with nonresponse. Eur J Stat Prob 9(1):32–42

    Google Scholar 

  • Iseh MJ, Bassey MO (2022) Calibration estimators for population mean with subsampling the nonrespondents under stratified sampling. Sci J Appl Math Stat 10(4):45–56

    Google Scholar 

  • Kim JK, Park M (2010) Calibration estimation in survey sampling. Int Stat Rev 78(1):21–39

    Article  Google Scholar 

  • Kott PS (2006) Using calibration weighting to adjust for nonresponse and coverage errors. Surv Methodol 32(2):133–142

    Google Scholar 

  • Koyuncu N, Kadilar C (2013) Calibration estimator using different distance measures in stratified random sampling. Int J Mod Eng Res 3(1):415–419

    Google Scholar 

  • Koyuncu N, Kadilar C (2016) Calibration weighting in stratified random sampling. Commun Stat Simul Comput ation 45:2267–2275

  • Montanari GE, Ranalli MG (2005) Nonparametric model calibration estimation in survey sampling. J Am Stat Assoc 100(472):1429–1442

    Article  MathSciNet  MATH  Google Scholar 

  • Murthy MN (1967) Sampling theory and methods, 1st edn. Statistical Publishing Society, Calcutta

    MATH  Google Scholar 

  • Ozgul N (2019) New calibration estimator based on two auxiliary variables in stratified sampling. Commun Stat Theory Methods 48(6):1481–1492

    Article  MathSciNet  MATH  Google Scholar 

  • Ozgul N (2020) New improved calibration estimator based on two auxiliary variables in stratified two-phase sampling. J Stat Comput Simul. https://doi.org/10.1080/00949655.2020.1844702

    Article  MathSciNet  MATH  Google Scholar 

  • Rai PK, Singh A, Qasim M (2021) Calibration-based estimators using different distance measures under two auxiliary variables: aA comparative study. J Mod Appl Stat Methods 19(1): 356 https://doi.org/10.22237/jmasm/1619481600

  • Rao D, Khan MGM, Khan S (2012) Mathematical programming on multivariate calibration estimation in stratified sampling. World Acad Sci Eng Technol 72:78–82

    Google Scholar 

  • Rueda M, Martínez S, Martínez H, Arcos A (2007) Estimation of the distribution function with calibration methods. J Stat Plan Inference 137:435–448

    Article  MathSciNet  MATH  Google Scholar 

  • Sarndal CE (2007) The calibration approach in survey theory and practice. Component Stat Canada 33(2):99–119

    Google Scholar 

  • Shahzad U, Ahmad I, Garcia-Luengo, Kumar A (2023a) Estimation of coeficient of variation using calibrated estimators in double startified random sampling. Mathematica 11:252

  • Shahzad U, Ahmad I, Alshahrani IM, Iftikhar S (2023b) Calibration-based mean estimators under stratified median ranked set sampling. Mathematics 11:1825

    Article  Google Scholar 

  • Singh S (2003) Advanced sampling theory with applications. How Michael ‘Selected’Amy. Kluwer Academic Publishers, Dordrecht

  • Singh S, Arnab R (2011) On calibration of design weights. Metron 69(2):185–205

    Article  MathSciNet  MATH  Google Scholar 

  • Singh HP, Tailor R (2003) Use of known correlation coefficient in estimating the finite population mean. Stat Trans 6:555–560

    Google Scholar 

  • Singh HP, Tailor R, Tailor R, Kakran M (2004) An improved estimator of population mean using power transformation. J Indian Soc Agric Stat 58:223–230

    MathSciNet  MATH  Google Scholar 

  • Sisodia BVS, Dwivedi VK (1981) A modified ratio estimator using coefficient of variation of auxiliary variable. J Indian Soc Agric Stat 33:13–18

    Google Scholar 

  • Subramani J, Kumarapandiyan GG (2012) Modified ratio estimators for population mean using function of quartiles of auxiliary variable. Bonfring Int J Ind Eng Manage Sci 2(2):19–23

    Google Scholar 

  • Taylor P, Théberge A, Theberge A (1999) Eextensions of calibration estimators in survey sampling. J Am Stat Assoc 94(446):37–41

    MATH  Google Scholar 

  • Wu C, Sitter RR (2001) A model-calibration approach to using complete auxiliary information from survey data. J Am Stat Assoc 96(453):185–193

    Article  MathSciNet  MATH  Google Scholar 

  • Yan Z, Tian B (2010) Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. Commun Comput Inf Sci 106(2):103–110

    Google Scholar 

  • Zaman T, Bulut H (2023) Robust calibration for estimating the population mean using stratified random sampling. Sci Iran. https://doi.org/10.24200/sci.2023.59408.6224

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Nigeria, Nsukka, Nigeria

    Abimibola V. Oladugba, Ayodeji S. Adubi, Fabian C. Okafor & Oluwagbenga T. Babatunde

  2. School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor, Penang, Malaysia

    Oluwagbenga T. Babatunde

  3. Department of Psychology, University of Nigeria, Nsukka, Nigeria

    Peace C. Adubi

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  1. Abimibola V. Oladugba
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  2. Ayodeji S. Adubi
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  3. Fabian C. Okafor
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  4. Oluwagbenga T. Babatunde
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  5. Peace C. Adubi
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Correspondence to Abimibola V. Oladugba.

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Oladugba, A.V., Adubi, A.S., Okafor, F.C. et al. Calibrated Estimators for Population Means Using Standard Deviation of the Auxiliary Variable. J Indian Soc Probab Stat 24, 565–579 (2023). https://doi.org/10.1007/s41096-023-00167-4

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