# A MODIFIED GENERALIZED CHAIN RATIO IN REGRESSION ESTIMATOR

## DOI:

https://doi.org/10.51406/jnset.v19i1.2087## Keywords:

Chain ratio, regression estimator: relative efficiency## Abstract

Generalized Chain ratio in regression type estimator is efficient for estimating the population mean. Many authors have derived a Generalized Chain ratio in regression type estimator. However, the computation of its Mean Square Error (MSE) is cumbersome based on the fact that several iterations have to be done, hence the need for a modified generalized chain ratio in regression estimator with lower MSE. This study proposed a modified generalized chain ratio in regression estimator which is less cumbersome in its computation. Two data sets were used in this study. The first data were on tobacco production by tobacco producing countries with yield of tobacco (variable of interest), area of land and production in metric tonnes as the auxiliary variables. The second data were the number of graduating pupils (variable of interest) in Ado-Odo/Ota local government, Ogun state with the number of enrolled pupils in primaries one and five as the auxiliary variables. The mean square errors in the existing and proposed estimators for various values of alpha were derived and relative efficiency was determined. The MSE for the existing estimator of tobacco production gave six values 0.0080, 0.0079, 0.0080, 0.0082, 0.0087 and 0.0093 with 0.0079 as the minimum while the proposed estimator gave 0.0054. The MSEs for the existing estimator for the graduating pupils were 20.73, 11.08, 7.49, 9.96, 18.50 and 33.10 with 7.49 as the minimum while the proposed was 6.52. The results of this study showed that the proposed estimator gave lower MSE for the two data sets, hence it is more efficient.

## References

Brewer, K.R., Hanif, M. 1970. Durbin’s new multistage variance estimator. Journal of the Royal Statistical Society, Series B. 32(2): 302-311.

Cassel, C.M., Särndal, C.E., Wretman, J.H. 1976. Some results on generalized difference estimation and generalized regression estimation for finite populations, Biometrika 63(3): 615–620. https://doi.org/10.1093/biomet/63.3.615.

Chand, L. 1975. Some Ratio-type Estimators based on two or more Auxiliary Variables. Unpublished Ph.D. Dissertation. Iowa State University, Iowa.

Cochran, W.G. 1977. Sampling Techniques (3rd Edition), New York, Wiley.

Holt, D., Smith, T.M.F. 1979. Post-stratification, J.R. Stat. Soc., A 142: 33-36.

Kadilar, C., Cingi, H. 2005. Ratio Estimators in Stratified Random Sampling. Communications in Statistics-Theory and Methods 34: 597-602.

Khare, B.B., Srivastava, U., Kumar, K. 2013. A generalized chain ratio in regression estimator for population mean using two auxiliary characters in sample survey. J. Sci. Res. 57: 147–153.

Kiregyera, B. 1984. Regression-type estimator using two auxiliary variables and model of double sampling from finite populations. Metrika 31: 215-226.

Mohanty, S. 1967. Combination of Regression and Ratio Estimate. Journal of Indian Statistical Association 5: 16-19.

Prasad, B. 1989. Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communication Statistical theory Method 18(1): 379-392.

Royall, R.M. 1970. On finite population theory under certain linear regression models. Biometrika 57: 377-387.

Särndal, C.E. 1980. On π-inverse weighting versus best linear unbiased weighting in probability sampling. Biometrika 67:639–650.

Särndal, C.E. 1982. Implications of survey design for generalized regression estimation of linear functions. J. Stat. Plan. Infer 7: 155–170.

Särndal, C.E., Swensson, B., Wretman J.H. 1992. Model assisted survey sampling. Springer, New York.

Sarndal, C.E., Swensson, B. 1987. A general view of estimation for two phases of selection with applications to two-phase sampling and nonresponse. International Statistics Review 55: 279-294.

Singh, S. 2003. Advanced sampling theory with applications: how Michael ‘selected’ Amy. 2nd Edition. Punjab Agricultural University Press.

Srivastava, S.R., Khare, B.B. 1990. A generalized chain ratio estimator for mean of finite population. J. Ind. Soc. Agri. Statist. 42(1): 108-117.