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

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

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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.

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Resumen

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

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Texto completo disponible en PDF

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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.

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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.

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

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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.

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

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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}
}

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