Published

2015-07-01

A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling

Una nota sobre el estimador exponencial generalizado para la varianza poblacional en muestreo de encuestas

DOI:

https://doi.org/10.15446/rce.v38n2.51667

Keywords:

Auxiliary Variable, Bias, Efficiency, Mean Square Error, Variance (en)
Error cuadrático medio, Sesgo, Variable auxiliar, Varianza, Eficiencia. (es)

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Authors

  • Javid Shabbir Quaid-i-Azam University, Islamabad, Pakistan
  • Sat Gupta The University of North Carolina at Greensboro, Greensboro, United States

Recently a new generalized estimator for population variance using information on the auxiliary variable has been introduced by Asghar, Sanaullah & Hanif (2014). In that paper there was some inaccuracy in the bias and MSE expressions. In this paper, we provide the correct expressions for bias and MSE of the Asghar et al. (2014) estimator, up to the first order of approximation. We also propose a new generalized exponential type estimator for population variance which performs better than the existing estimators. Four data sets are used for numerical comparison of efficiencies.

Recientemente, un nuevo estimador generalizado de varianza de la población utilizando información sobre la variable auxiliar ha sido introducida por Asghar et al. (2014). En ese documento había alguna inexactitud en las expresiones de sesgo y ECM. En este trabajo, proporcionamos las expresiones correctas de sesgo y ECM de Asghar et al. (2014) hasta el primer orden de aproximación. También proponemos un nuevo estimador tipo exponencial generalizado de la varianza de la población que se comporta mejor que los estimadores existentes. Cuatro conjuntos de datos se utilizan para la comparación
numérica de la eficiencia.

https://doi.org/10.15446/rce.v38n2.51667

A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling

Una nota sobre el estimador exponencial generalizado para la varianza poblacional en muestreo de encuestas

JAVID SHABBIR1, SAT GUPTA2

1Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Professor. Email: javidshabbir@gmail.com
2The University of North Carolina at Greensboro, Department of Mathematics and Statistics, Greensboro, United States. Professor. Email: sngupta@uncg.edu


Abstract

Recently a new generalized estimator for population variance using information on the auxiliary variable has been introduced by Asghar et al. (2014). In that paper there was some inaccuracy in the bias and MSE expressions. In this paper, we provide the correct expressions for bias and MSE of the Asghar et al. (2014) estimator, up to the first order of approximation. We also propose a new generalized exponential type estimator for population variance which performs better than the existing estimators. Four data sets are used for numerical comparison of efficiencies.

Key words: Auxiliary Variable, Bias, Efficiency, Mean Square Error, Variance.


Resumen

Recientemente, un nuevo estimador generalizado de varianza de la población utilizando información sobre la variable auxiliar ha sido introducida por Asghar et al. (2014). En ese documento había alguna inexactitud en las expresiones de sesgo y ECM. En este trabajo, proporcionamos las expresiones correctas de sesgo y ECM de Asghar et al. (2014) hasta el primer orden de aproximación. También proponemos un nuevo estimador tipo exponencial generalizado de la varianza de la población que se comporta mejor que los estimadores existentes. Cuatro conjuntos de datos se utilizan para la comparación numérica de la eficiencia.

Palabras clave: error cuadrático medio, sesgo, variable auxiliar, varianza, eficiencia.


Texto completo disponible en PDF


References

1. Asghar, A., Sanaullah, A. & Hanif, M. (2014), 'Generalized exponential type estimator for population variance in survey sampling', Revista Colombiana de Estadística 7(1), 211-222.

2. Bansal, M., Javed, M. & Khanna, N. (2011), 'A class of estimators of variance of the regression estimator', International Journal of Agriculture and Statistical Sciences 7(1), 275-279.

3. Cochran, W. G. (1977), Sampling Techniques, 3 edn, Jhon Wiley & Sons, New York.

4. Gupta, S. & Shabbir, J. (2008), 'Variance estimation in simple random sampling using auxiliary information', Hacettepe Journal of Mathematics and Statistics 37(1), 57-67.

5. Isaki, C. T. (1983), 'Variance estimation using auxiliary information', Journal of the American Statistical Association 78(381), 117-123.

6. Jhajj, H. S., Sharma, M. K. & Grover, L. K. (2005), 'An efficient class of chain estimators of population variance under sub-sampling scheme', Journal of the Japan Statistical Society 35(2), 273-286.

7. Kadilar, C. & Cingi, H. (2006), 'Ratio estimators for the population variance in simple and stratified random sampling', Applied Mathematics and Computation 173(2), 1047-1059.

8. Murthy, M. N. (1967), Sampling Theory and Methods, Statistical Publishing Society, Calcutta.

9. Nayak, R. & Sahoo, L. (2012), 'Some alternative predictive estimators of population-variance', Revista Colombiana de Estadística 35(3), 509-521.

10. Sarndal, C. E., Swensson, B. & Wretman, J. H. (1992), Model Asssisted Survey Sampling, Springer Verlag, New York.

11. Shabbir, J., Haq, A. & Gupta, S. (2014), 'A new difference-cum-exponential type estimator of finite population mean in simple random sampling', Revista Colombiana de Estadística 37(1), 199-211.

12. Singh, H. P., Upadhyaya, L. N. & Namjoshi, U. D. (1988), 'Estimation of finite population variance', Current Science 57(24), 1331-1334.

13. Singh, R., Chauhan, P., Swan, N. & Smarandache, F. (2011), 'Improved exponential estimator for population variance using two auxiliary variables', Italian Journal of Pure and Applied Mathematics 28, 101-108.

14. Subramani, J. & Kumarapandiyan, G. (2012), 'Variance estimation using median of the auxiliary variable', International Journal of Probability and Statistics 1(3), 36-40.

15. Upadhyaya, L. N., Singh, H. P., Chatterjee, S. & Yadav, R. (2011), 'Improved ratio and product exponential type estimators', Journal of Statistical Theory and Practice 5(2), 285-302.

16. Yadav, S. K. & Kadilar, C. (2013), 'Improved exponential type ratio estimator of population variance', Revista Colombiana de Estadística 36(1), 145-152.

17. Yadav, S. K. & Kadilar, C. (2014), 'A two parameter variance estimator using auxiliary information', Applied Mathematics and Computation 226, 117-122.


[Recibido en julio de 2014. Aceptado en enero de 2015]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n2a05,
    AUTHOR  = {Shabbir, Javid and Gupta, Sat},
    TITLE   = {{A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {2},
    pages   = {385-397}
}

References

Asghar, A., Sanaullah, A. & Hanif, M. (2014), ‘Generalized exponential type estimator for population variance in survey sampling’, Revista Colombiana de Estadística 7(1), 211–222.

Bansal, M., Javed, M. & Khanna, N. (2011), ‘A class of estimators of variance of the regression estimator’, International Journal of Agriculture and Statistical Sciences 7(1), 275–279.

Cochran, W. G. (1977), Sampling Techniques, 3 edn, Jhon Wiley & Sons, New York.

Gupta, S. & Shabbir, J. (2008), ‘Variance estimation in simple random sampling using auxiliary information’, Hacettepe Journal of Mathematics and Statistics 37(1), 57–67.

Isaki, C. T. (1983), ‘Variance estimation using auxiliary information’, Journal of the American Statistical Association 78(381), 117–123.

Jhajj, H. S., Sharma, M. K. & Grover, L. K. (2005), ‘An efficient class of chain estimators of population variance under sub-sampling scheme’, Journal of the Japan Statistical Society 35(2), 273–286.

Kadilar, C. & Cingi, H. (2006), ‘Ratio estimators for the population variance in simple and stratified random sampling’, Applied Mathematics and Computation 173(2), 1047–1059.

Murthy, M. N. (1967), Sampling Theory and Methods, Statistical Publishing Society, Calcutta.

Nayak, R. & Sahoo, L. (2012), ‘Some alternative predictive estimators of population variance’, Revista Colombiana de Estadística 35(3), 509–521.

Sarndal, C. E., Swensson, B. & Wretman, J. H. (1992), Model Asssisted Survey Sampling, Springer Verlag, New York.

Shabbir, J., Haq, A. & Gupta, S. (2014), ‘A new difference-cum-exponential type estimator of finite population mean in simple random sampling’, Revista Colombiana de Estadística 37(1), 199–211.

Singh, H. P., Upadhyaya, L. N. & Namjoshi, U. D. (1988), ‘Estimation of finite population variance’, Current Science 57(24), 1331–1334.

Singh, R., Chauhan, P., Swan, N. & Smarandache, F. (2011), ‘Improved exponential estimator for population variance using two auxiliary variables’, Italian Journal of Pure and Applied Mathematics 28, 101–108.

Subramani, J. & Kumarapandiyan, G. (2012), ‘Variance estimation using median of the auxiliary variable’, International Journal of Probability and Statistics 1(3), 36–40.

Upadhyaya, L. N., Singh, H. P., Chatterjee, S. & Yadav, R. (2011), ‘Improved ratio and product exponential type estimators’, Journal of Statistical Theory and Practice 5(2), 285–302.

Yadav, S. K. & Kadilar, C. (2013), ‘Improved exponential type ratio estimator of population variance’, Revista Colombiana de Estadística 36(1), 145–152.

Yadav, S. K. & Kadilar, C. (2014), ‘A two parameter variance estimator using auxiliary information’, Applied Mathematics and Computation 226, 117–122.

How to Cite

APA

Shabbir, J. and Gupta, S. (2015). A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling. Revista Colombiana de Estadística, 38(2), 385–397. https://doi.org/10.15446/rce.v38n2.51667

ACM

[1]
Shabbir, J. and Gupta, S. 2015. A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling. Revista Colombiana de Estadística. 38, 2 (Jul. 2015), 385–397. DOI:https://doi.org/10.15446/rce.v38n2.51667.

ACS

(1)
Shabbir, J.; Gupta, S. A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling. Rev. colomb. estad. 2015, 38, 385-397.

ABNT

SHABBIR, J.; GUPTA, S. A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling. Revista Colombiana de Estadística, [S. l.], v. 38, n. 2, p. 385–397, 2015. DOI: 10.15446/rce.v38n2.51667. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/51667. Acesso em: 29 mar. 2024.

Chicago

Shabbir, Javid, and Sat Gupta. 2015. “A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling”. Revista Colombiana De Estadística 38 (2):385-97. https://doi.org/10.15446/rce.v38n2.51667.

Harvard

Shabbir, J. and Gupta, S. (2015) “A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling”, Revista Colombiana de Estadística, 38(2), pp. 385–397. doi: 10.15446/rce.v38n2.51667.

IEEE

[1]
J. Shabbir and S. Gupta, “A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling”, Rev. colomb. estad., vol. 38, no. 2, pp. 385–397, Jul. 2015.

MLA

Shabbir, J., and S. Gupta. “A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling”. Revista Colombiana de Estadística, vol. 38, no. 2, July 2015, pp. 385-97, doi:10.15446/rce.v38n2.51667.

Turabian

Shabbir, Javid, and Sat Gupta. “A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling”. Revista Colombiana de Estadística 38, no. 2 (July 1, 2015): 385–397. Accessed March 29, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/51667.

Vancouver

1.
Shabbir J, Gupta S. A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling. Rev. colomb. estad. [Internet]. 2015 Jul. 1 [cited 2024 Mar. 29];38(2):385-97. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/51667

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CrossRef citations7

1. Amber Asghar, Aamir Sanaullah, Muhammad Hanif. (2018). A multivariate regression-cum-exponential estimator for population variance vector in two phase sampling. Journal of King Saud University - Science, 30(2), p.223. https://doi.org/10.1016/j.jksus.2017.01.010.

2. Amber Asghar, Aamir Sanaullah, Hina Khan, Muhammad Hanif. (2023). Comparative Analysis of Variance Estimation Methods in Two-Phase Sampling: A Focus on Regression-cum-Exponential Estimators with Multiple Auxiliaries. Bulletin of Business and Economics (BBE), 12(3), p.573. https://doi.org/10.61506/01.00071.

3. Sana Kaleem, Hina Khan, Muhammad Aslam. (2020). Generalized regression cum ratio estimators of population variance in two phase sampling. Journal of Statistics and Management Systems, 23(3), p.663. https://doi.org/10.1080/09720510.2019.1675293.

4. Saman Hanif Shahbaz, Aisha Fayomi, Muhammad Qaiser Shahbaz. (2023). Estimation of the general population parameter in single- and two-phase sampling. AIMS Mathematics, 8(7), p.14951. https://doi.org/10.3934/math.2023763.

5. Muhammad Hanif, Usman Shahzad. (2019). Estimation of population variance using kernel matrix. Journal of Statistics and Management Systems, 22(3), p.563. https://doi.org/10.1080/09720510.2019.1565444.

6. Aamir Sanaullah, Iqra Niaz, Javid Shabbir, Iqra Ehsan. (2022). A class of hybrid type estimators for variance of a finite population in simple random sampling. Communications in Statistics - Simulation and Computation, 51(10), p.5609. https://doi.org/10.1080/03610918.2020.1776873.

7. Housila P. Singh, Diksha Arya, Subhash Kumar Yadav. (2023). Optimal Strategy for Improved Estimation of Population Variance Using Known Auxiliary Parameters. International Journal of Applied and Computational Mathematics, 9(5) https://doi.org/10.1007/s40819-023-01559-7.

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