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

Keywords:

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

Downloads

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.

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.

License

Copyright (c) 2015 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).