Separate-Type Estimators for Estimating Population Ratio in Post-Stratified Sampling Using Variable Transformation

ABSTRACT

The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.

The study proposes, along the line of [1], six separate-type estimators for estimating the population ratio of two variables in post-stratified sampling, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations, both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions, under which the proposed separate-type estimators would perform better than the associated customary separate-type estimators in terms of having smaller mean squared errors, were obtained. Furthermore, conditions under which some of the proposed separate-type estimators would perform better than other proposed separate-type estimators were also obtained. The optimum estimators among the proposed separate-type estimators were obtained and an empirical illustration confirmed the theoretical results.

KEYWORDS

Variable Transformation, Separate-Type Estimator, Optimum Estimators, Ratio, Product and Regression-Type Estimators, Mean Squared Error

Variable Transformation, Separate-Type Estimator, Optimum Estimators, Ratio, Product and Regression-Type Estimators, Mean Squared Error

Cite this paper

Onyeka, A. , Izunobi, C. and Iwueze, I. (2015) Separate-Type Estimators for Estimating Population Ratio in Post-Stratified Sampling Using Variable Transformation.*Open Journal of Statistics*, **5**, 27-34. doi: 10.4236/ojs.2015.51004.

Onyeka, A. , Izunobi, C. and Iwueze, I. (2015) Separate-Type Estimators for Estimating Population Ratio in Post-Stratified Sampling Using Variable Transformation.

References

[1] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2013) Estimation of Population Ratio in Simple Random Sampling Using Variable Transformation. Global Journal of Science Frontier Research, 13, 57-65.

[2] Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. The Journal of Agricultural Science, 30, 262-275.

http://dx.doi.org/10.1017/S0021859600048012

[3] Robson, D.S. (1957) Application of Multivariate Polykays to the Theory of Unbiased Ratio-Type Estimation. Journal of the American Statistical Association, 52, 511-522.

http://dx.doi.org/10.1080/01621459.1957.10501407

[4] Murthy, M.N. (1964) Product Method of Estimation. Sankhya, Series A, 26, 294-307.

[5] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya, Series B, 27, 321-328.

[6] Sukhatme, P.V. and Sukhatme, B.V. (1970) Sampling Theory of Surveys with Applications. Iowa State University Press, Ames.

[7] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley & Sons, New York.

[8] Onyeka, A.C. (2013) Dual to Ratio Estimators of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameters. Global Journal of Science Frontier Research, 13, 13-23.

[9] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation. Open Journal of Statistics, 4, 284-291.

http://dx.doi.org/10.4236/ojs.2014.44029

[10] Srivenkataramana, T. (1980) A Dual of Ratio Estimator in Sample Surveys. Biometrika, 67, 199-204.

http://dx.doi.org/10.1093/biomet/67.1.199

[11] Upadhyaya, L.N., Singh, G.N. and Singh, H.P. (2000) Use of Transformed Auxiliary Variable in the Estimation of Population Ratio in Sample Survey. Statistics in Transition, 4, 1019-1027.

[12] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Characters. Statistica, Anno LXV, 4, 407-418.

[13] Tailor, R. and Sharma, B.K. (2009) A Modified Ratio-Cum-Product Estimator of Finite Population Mean Using Known Coefficient of Variation and Coefficient of Kurtosis. Statistics in Transition—New Series, 10, 15-24.

[14] Sharma, B. and Tailor, R. (2010) A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling. Global Journal of Science Frontier Research, 10, 27-31.

[1] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2013) Estimation of Population Ratio in Simple Random Sampling Using Variable Transformation. Global Journal of Science Frontier Research, 13, 57-65.

[2] Cochran, W.G. (1940) The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. The Journal of Agricultural Science, 30, 262-275.

http://dx.doi.org/10.1017/S0021859600048012

[3] Robson, D.S. (1957) Application of Multivariate Polykays to the Theory of Unbiased Ratio-Type Estimation. Journal of the American Statistical Association, 52, 511-522.

http://dx.doi.org/10.1080/01621459.1957.10501407

[4] Murthy, M.N. (1964) Product Method of Estimation. Sankhya, Series A, 26, 294-307.

[5] Singh, M.P. (1965) On the Estimation of Ratio and Product of the Population Parameters. Sankhya, Series B, 27, 321-328.

[6] Sukhatme, P.V. and Sukhatme, B.V. (1970) Sampling Theory of Surveys with Applications. Iowa State University Press, Ames.

[7] Cochran, W.G. (1977) Sampling Techniques. 3rd Edition, John Wiley & Sons, New York.

[8] Onyeka, A.C. (2013) Dual to Ratio Estimators of Population Mean in Post-Stratified Sampling Using Known Value of Some Population Parameters. Global Journal of Science Frontier Research, 13, 13-23.

[9] Onyeka, A.C., Nlebedim, V.U. and Izunobi, C.H. (2014) A Class of Estimators for Population Ratio in Simple Random Sampling Using Variable Transformation. Open Journal of Statistics, 4, 284-291.

http://dx.doi.org/10.4236/ojs.2014.44029

[10] Srivenkataramana, T. (1980) A Dual of Ratio Estimator in Sample Surveys. Biometrika, 67, 199-204.

http://dx.doi.org/10.1093/biomet/67.1.199

[11] Upadhyaya, L.N., Singh, G.N. and Singh, H.P. (2000) Use of Transformed Auxiliary Variable in the Estimation of Population Ratio in Sample Survey. Statistics in Transition, 4, 1019-1027.

[12] Singh, H.P. and Tailor, R. (2005) Estimation of Finite Population Mean Using Known Correlation Coefficient between Auxiliary Characters. Statistica, Anno LXV, 4, 407-418.

[13] Tailor, R. and Sharma, B.K. (2009) A Modified Ratio-Cum-Product Estimator of Finite Population Mean Using Known Coefficient of Variation and Coefficient of Kurtosis. Statistics in Transition—New Series, 10, 15-24.

[14] Sharma, B. and Tailor, R. (2010) A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling. Global Journal of Science Frontier Research, 10, 27-31.