A Generalised Family of Estimator for Estimating Unknown Variance Using Two Auxiliary Variables

Viplav Kumar Singh; Rajesh Singh

doi:10.15415/mjis.2015.32017

Authors

Viplav Kumar Singh Department of Statistics, Banaras Hindu University, Varanasi -221005, India
Rajesh Singh Department of Statistics, Banaras Hindu University, Varanasi -221005, India

DOI:

https://doi.org/10.15415/mjis.2015.32017

Keywords:

Proposed estimator, Double sampling technique, Bias(B), Mean Square Error (MSE), Optimum estimator

Abstract

The present study deals with the estimation of unknown variance using two auxiliary variates under simple random sampling without replacement (SRSWOR) scheme. We have also extended our work to the case of the double sampling scheme. The asymptotic expressions for the mean squared errors of the proposed estimators are derived and their optimum values have been obtained. A comparison between the existing and the proposed class of estimators of S_y² has been made empirically with the help of two population data taken from [1] and [10].

Downloads

Download data is not yet available.

References

A Ahmed M.S.: Some Estimation Procedure Using Multivariate Auxiliary Information in Sample Surveys. Ph.D. thesis, Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh-202002, India (1995).

G Grover, L. K .: A correction note on improvement in variance estimation using auxiliary information. Commun. Stat. Theo. Meth. 39:753–764 (2010).

http://dx.doi.org/10.1080/03610920902785786

Isaki, C.T.: Variance estimation using auxiliary information. J. Amer. Statist. Assoc.78:117–123 (1983). http://dx.doi.org/10.1080/01621459.1983.10477939

Jhajj, H .S., Sharma, M. K. and Grover, L. K.: An efficient class of chain estimators of population variance under the sub-sampling scheme. J. Japan Stat. Soc., 35(2), 273-286 (2005). http://dx.doi.org/10.14490/jjss.35.273

Kadilar, C., Cingi, H.: Improvement in variance estimation using auxiliary information. Hacettepe J. Math. Statist. 35(1):111–115 (2006).

Kadilar, C., Cingi, H.: Improvement in variance estimation in simple random sampling. Commun. Statist. Theory. Meth. 36:2075–2081(2007).

http://dx.doi.org/10.1080/03610920601144046

Kadilar, C., Cingi, H.: A new estimator using two auxiliary variables. Applied mathematics and computation 162 901-908 (2005). http://dx.doi.org/10.1016/j.amc.2003.12.130

Koyuncu, N.: Improved estimation of population mean in stratified random sampling using the information on the auxiliary attribute. Proceeding of 59-th ISI world Statistics Congress, Hong Kong, China, August, pp: 25-30 (2013).

L Lu, J., Yan, Z., Ding, C., Hong, Z.: The chain ratio estimator using two auxiliary information. International Conference on Computer and Communication Technologies in Agriculture Engineering 586-589 (2010).

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

Shabbir, J. and Gupta, S.: On improvement in variance estimation using auxiliary information. Commun. Statist. Theor. Meth. 36(12):2177–2185 (2007).

http://dx.doi.org/10.1080/03610920701215092

Singh, H.P. and Singh, R.: Improved ratio-type estimator for variance using auxiliary information. J Indian Soc Agric Stat 54(3):276–287 (2001).

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

Singh, H. P. and Solanki, R.S.: A new procedure for variance estimation in simple random sampling using auxiliary information. Stat. Paps. DOI 10.1007/s00362-012-0445-2 (2012). http://dx.doi.org/10.1007/s00362-012-0445-2

Singh, R., Chauhan, P., Sawan, N.: On the linear combination of Ratio-product type exponential estimator for estimating a finite population means. Statistics in Transition 9(1) -115 (2008a).

Singh, R., Chauhan, P., Sawan, N. and Smarandache, F.: Almost unbiased ratio and product type estimator of finite population variance using the knowledge of kurtosis of an auxiliary variable in sample surveys. Octogon Mathematical Journal, Vol. 16, No. 1, 123-130 (2008b).

Singh, R., Kumar, M., Smarandache, F.: Almost Unbiased Estimator for Estimating Population Mean Using Known Value of Some Population Parameter(s); Pak.j.stat.oper.res. 76 ( 2), 63-76 (2008).

Singh, R., Chauhan, P., Sawan, N. and Smarandache, F.: Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables. Italian Jour. Of Pure and Appld. Math., 28, 103-110(2011).

Singh, V. K., Singh, R. and Florentin, S.: Some improved estimators for population variance using two auxiliary variables in double sampling. on improvement in estimating population parameter(s) using auxiliary information. Educational Publishing & Journal of Matter Regularity (Beijing) (2013).

Singh, V. K., Singh, R.: Predictive estimation of finite population mean using generalised family of estimators, accepted in JTSA(2014).