RATIO ESTIMATORS FOR POPULATION MEAN USING ROBUST REGRESSION IN DOUBLE SAMPLING

Year 2016, Volume: 29 Issue: 4, 793 - 798, 19.12.2016

Muhammad Noor-ul-amin Muhammad Qaiser Shahbaz Cem Kadılar

Abstract

In this study, ratio estimators for the population mean are suggested using the robust regression under the double sampling scheme. The mean squared error (MSE) expressions are obtained for the first degree of approximation. Theoretical comparisons show that the proposed estimators having the robust regression estimates are more efficient than the estimators using the least square method under the certain conditions. Theoretical findings are supported with the aid of a real life dataset in application and a simulation study is also conducted to evaluate the performance of the proposed estimators.

Keywords

Auxiliary information, double sampling, robust regression.

References

• Chand, L., “Some Ratio-Type Estimator Based on Two or More Auxiliary Variables”, Unpublished Ph.D. dissertation, Iowa State University, Iowa. (1975).
• Choudhury, S. and Singh, B. K., “A class of chain ratio-product type estimators with two auxiliary variables under double sampling scheme”. Journal of the Korean Statistical Society, 41(2); 247-256, (2012).
• Grover, L.K., Kaur. P. and Vishwakarma, G.K. “Product type exponential estimators of population mean under linear transformation of auxiliary variable in simple random sampling”. Applied Mathematics and Computations, 219; 1937-1946, (2012).
• Huber, P. H., “Robust estimation of a location parameter”, The Annals of Mathematical Statistics”, 73-101, (1964).
• Kadilar, C. and Cingi, H., “Ratio estimators in simple random sampling”, Applied Mathematics and Computation, 151; 893-902, (2004).
• Kadilar, C., Candan, M., and Cingi, H. “Ratio estimators using robust regression”, Hacettepe Journal of Mathematics and Statistics, 36 (2); 181-188, (2007).
• Kiregyera, B., “A chain ratio-type estimator in finite population double sampling using two auxiliary variables”, Metrika, 27;217–223, (1980).
• Kiregyera, B., “Regression-type estimators using two auxiliary variables and model of double sampling from finite populations”, Metrika, 31; 215–226, (1984).
• Noor ul Amin, M. and Hanif, M., “Some exponential estimators in survey sampling”, Pakistan Journal of Statistics, 28 (3); 367–374, (2012).
• Sanaullah, A., Ali H. A., Noor ul Amin, M., and Hanif, M., “Generalized exponential chain ratio estimators under stratified two-phase random sampling”. Applied Mathematics and Computation, 226; 541– 547, (2014).
• Singh, H. P. and Vishwakarma, G. K., “Modified exponential ratio and product estimators for finite population mean in double sampling”, Austrian Journal of Statistics, 36 (3); 217–225, (2007).
• Srivenkataramana, T. and Tracy, D. S., “Two-phase sampling for selection with probability proportional to size in sample surveys”, Biometrika, 76(4); 818–821, (1989).
• Vishwakarma, G. K. and Gangele, R. K., “A class of chain ratio-type exponential estimators in double sampling using two auxiliary variates”, Applied Mathematics and Computation, 227; 171-175, (2014).