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A new procedure for variance estimation in simple random sampling using auxiliary information

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  • Housila Singh
  • Ramkrishna Solanki

Abstract

In this article we have envisaged an efficient generalized class of estimators for finite population variance of the study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of the bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator in the proposed class of estimators has been identified with its mean square error formula. We have shown that the proposed class of estimators is more efficient than the usual unbiased, difference, Das and Tripathi (Sankhya C 40:139–148, 1978 ), Isaki (J. Am. Stat. Assoc. 78:117–123, 1983 ), Singh et al. (Curr. Sci. 57:1331–1334, 1988 ), Upadhyaya and Singh (Vikram Math. J. 19:14–17, 1999b ), Kadilar and Cingi (Appl. Math. Comput. 173:2, 1047–1059, 2006a ) and other estimators/classes of estimators. In the support of the theoretically results we have given an empirical study. Copyright Springer-Verlag 2013

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  • Housila Singh & Ramkrishna Solanki, 2013. "A new procedure for variance estimation in simple random sampling using auxiliary information," Statistical Papers, Springer, vol. 54(2), pages 479-497, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:479-497
    DOI: 10.1007/s00362-012-0445-2
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    References listed on IDEAS

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    1. Housila P. Singh & L.N. Upadhyaya & Rajesh Tailor, 2009. "Ratio-cum-product type exponential estimator," Statistica, Department of Statistics, University of Bologna, vol. 69(4), pages 299-310.
    2. A. Cebrián & M. García, 1997. "Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 171-178, January.
    3. Housila Singh & Rajesh Tailor & Sarjinder Singh & Jong-Min Kim, 2008. "A modified estimator of population mean using power transformation," Statistical Papers, Springer, vol. 49(1), pages 37-58, March.
    4. M. Singh, 1967. "Ratio cum product method of estimation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 12(1), pages 34-42, December.
    5. Housila P. Singh & Gajendra K. Vishwakarma, 2010. "A general procedure for estimating the population mean in stratified sampling using auxiliary information," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 47-65.
    6. M. Garcia & A. Cebrian, 1996. "Repeated substitution method: The ratio estimator for the population variance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 101-105, December.
    7. Nursel Koyuncu & Cem Kadilar, 2010. "On improvement in estimating population mean in stratified random sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 999-1013.
    8. Giancarlo Diana & Marco Giordan & Pier Perri, 2011. "An improved class of estimators for the population mean," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 123-140, June.
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    1. Singh Housila P. & Pal Surya K., 2016. "A New Family of Estimators of the Population Variance using Information on Population Variance of Auxiliary Variable in Sample Surveys," Statistics in Transition New Series, Statistics Poland, vol. 17(4), pages 605-630, December.
    2. Housila P. Singh & Surya K. Pal, 2016. "A New Family Of Estimators Of The Population Variance Using Information On Population Variance Of Auxiliary Variable In Sample Surveys," Statistics in Transition New Series, Polish Statistical Association, vol. 17(4), pages 605-630, December.
    3. Umer Daraz & Mohammed Ahmed Alomair & Olayan Albalawi & Abdulaziz S. Al Naim, 2024. "New Techniques for Estimating Finite Population Variance Using Ranks of Auxiliary Variable in Two-Stage Sampling," Mathematics, MDPI, vol. 12(17), pages 1-14, September.
    4. Umer Daraz & Jinbiao Wu & Olayan Albalawi, 2024. "Double Exponential Ratio Estimator of a Finite Population Variance under Extreme Values in Simple Random Sampling," Mathematics, MDPI, vol. 12(11), pages 1-11, June.
    5. Etebong P C, 2018. "Improved Family of Ratio Estimators of Finite Population Variance in Stratified Random Sampling," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(2), pages 48-53, February.
    6. Mohammed Ahmed Alomair & Umer Daraz, 2024. "Dual Transformation of Auxiliary Variables by Using Outliers in Stratified Random Sampling," Mathematics, MDPI, vol. 12(18), pages 1-16, September.

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