Improved Exponential Type Ratio Estimator of Population Variance

Estimador tipo razón exponencial mejorado para la varianza poblacional

This article considers the problem of estimating the population variance using auxiliary information. An improved version of Singh’s exponential type ratio estimator has been proposed and its properties have been studied under large sample approximation. It is shown that the proposed exponential type ratio estimator is more efficient than that considered by the Singh estimator, conventional ratio estimator and the usual unbiased estimator under some realistic conditions. An empirical study has been carried out to judge the merits of the suggested estimator over others.

Este artículo considera el problema de estimar la varianza poblacional usando información auxiliar. Una versión mejorada de un estimador exponencial tipo razón de Singh ha sido propuesta y sus propiedades han sido estudiadas bajo aproximaciones de grandes muestras. Se muestra que el estimador exponencial tipo razón propuesto es más eficiente que el estimador de Singh, el estimador de razón convencional y el estimador insesgado usual bajo algunas condiciones realísticas. Un estudio empírico se ha llevado a cabo con el fin de juzgar los méritos del estimador sugerido sobre otros disponibles.

Improved Exponential Type Ratio Estimator ofPopulation Variance Estimador tipo razón exponencial mejorado para la varianza poblacional SUBHASH KUMAR YADAV¹, CEM KADILAR²

¹Dr. Rml Avadh University, Department of Mathematics & Statistics (A Centre of Excellence), Faizabad, India. Assistant professor. Email: drskystats@gmail.com
²Hacettepe University, Department of Statistics, Ankara, Turkey. Professor. Email: kadilar@hacettepe.edu.tr

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Abstract

\noindent This article considers the problem of estimating the population variance using auxiliary information. An improved version of Singhs exponential type ratio estimator has been proposed and its properties have been studied under large sample approximation. It is shown that the proposed exponential type ratio estimator is more efficient than that considered by the Singh estimator, conventional ratio estimator and the usual unbiased estimator under some realistic conditions. An empirical study has been carried out to judge the merits of the suggested estimator over others.

Key words: Auxiliary variable, Bias, Efficiency, Mean squared error.

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Resumen

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

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Texto completo disponible en PDF

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References

1. Isaki, C. (1983), 'Variance estimation using auxiliary information', Journal of the American Statistical Association 78, 117-123.

2. Murthy, M. (1967), Sampling Theory and Methods, Calcutta Statistical Publishing Society, Kolkatta, India.

3. Nayak, R. & Sahoo, L. (2012), 'Some alternative predictive estimators of population variance', Revista Colombiana de Estadistica 35(3), 507-519.

4. Reddy, V. (1973), 'On ratio and product methods of estimation', Sankhya Serie B 35(3), 307-316.

5. Reddy, V. (1974), 'On a transformed ratio method of estimation', Sankhya Serie C 36, 59-70.

6. Singh, H. & Karpe, N. (2010), 'Estimation of mean, ratio and product using auxiliary information in the presence of measurement errors in sample surveys', Journal of Statistical Theory and Practice 4(1), 111-136.

7. Singh, H. & Kumar, S. (2008), 'A general family of estimators of finite population ratio, product and mean using two phase sampling scheme in the presence of non-response', Journal of Statistical Theory and Practice 2(4), 677-692.

8. Singh, H. & Singh, R. (2001), 'Improved ratio-type estimator for variance using auxiliary information', Journal of Indian Society of Agricultural Statistics 54(3), 276-287.

9. Singh, H. & Singh, R. (2003), 'Estimation of variance through regression approach in two phase sampling', Aligarh Journal of Statistics 23, 13-30.

10. Singh, H. & Vishwakarma, G. (2008), 'Some families of estimators of variance of stratified random sample mean using auxiliary information', Journal of Statistical Theory and Practice 2(1), 21-43.

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

12. Srivenkataramana, T. & Tracy, D. (1980), 'An alternative to ratio method in sample surveys', Annals of the Institute of Statistical Mathematics 32, 111-120.

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

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

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[Recibido en agosto de 2012. Aceptado en mayo de 2013]

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

@ARTICLE{RCEv36n1a08,
    AUTHOR  = {Yadav, Subhash Kumar and Kadilar, Cem},
    TITLE   = {{Improved Exponential Type Ratio Estimator ofPopulation Variance}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2013},
    volume  = {36},
    number  = {1},
    pages   = {145-152}
}

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