Synthetic Estimators Using Auxiliary Information in Small Domains

• Authors: Rai P. K. , Pandey K. K.
• Languages of publication: EN

Abstracts

EN

In the present article we discuss the generalized class of synthetic estimators for estimating the population mean of small domains under the information of two auxiliary variables, and describe the special cases under the different values of the constant beta involved in the proposed generalized class of synthetic estimator. In addition we have taken a numerical illustration for the two auxiliary variables and compared the result for the synthetic ratio estimator under single and two auxiliary variables.

Keywords

EN

auxiliary information; small area (domain) estimation synthetic estimation; optimum weights

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2013
• Volume: 14
• Issue: 1
• Pages: 31-44

Contributors

author

Rai P. K.

• Banasthali University

author

Pandey K. K.

• University of Petroleum & Energy Studies (UPES)

References

• AGRAWAL, M. C. and ROY, D. C., (1997). Efficient Estimators for Small Domains. Jour. Ind. Soc. Ag. Statistics 52(3), 327-337.
• GHOSH, M. and RAO, J. N. K., (1994). Small Area Estimation: An Appraisal. Statistical Science, 9, 55-93.
• GONZALEZ, M. E., (1973). Use and Evaluation of Synthetic Estimates. Proceedings of the Social Statistical Section of American Statistical Association, 33-36.
• GONZALEZ, M. E. and WAKSBERG, J., (1973). Estimation of the Error of Synthetic Estimates. Paper presented at first meeting of the International Association of Survey Statisticians, Vienna, Austria, 18-25, August 1973.
• HEDAYAT, A. S. and SINHA, B. K., (1991). Design and Inference in Finite Population Sampling. John Wiley and Sons, New York.
• PANDEY, KRISHAN K. and TIKKIWAL, G. C., (2010). ,,Generalized class of synthetic estimators for small area under systematic sampling design” Statistics in Transition-new series, Poland, Vol.11 No.1, pp. 75-89.
• PANDEY, KRISHAN, K., (2010). ,,Aspects of small area estimation using auxiliary information”. Book published by VDM Verlag Dr. Muller GmbH & Co. KG, Germany. (ISBN: 978-3-639-31569-1).
• PLATEK, R., RAO, J. N. K., SARNDAL, C. E. and SINGH, M. P., (1987). Small Area Statistics: An International Symposium. John Wiley and Sons, New York.
• PURCELL, N. J. and KISH, L., (1979). Estimation for Small Domain. Biometrics, 35, 365-384.
• SARNDAL, C. E., SWENSSON, B. and WRETMAN, J., (1992). Model Assisted Survey Sampling. Springer-Verlag, New York.
• SCHAIBLE, W. L., BROCK, D. B., CASADY, R. J. and SCHNACK, G. A., (1977). An Empirical Comparison of the Simple Inflation, Synthetic and Composite Estimators for Small Area Statistics. Proceedings of the American Statistical Association, Social Statistics Section, 1017-1021.
• SINGH, M. P., GAMBINO, J. and MANTEL, H., (1993). Issues and Options in the Provision of Small Area Data. Proceedings of International Scientific Conference on Small Area Statistics and survey Design (Held in September, 1992 in Warsaw, Poland), 37-75.
• SRIVASTAVA, S. K., (1967). An estimator using auxiliary information in sample surveys, Calcutta Statistical Association Bulletin, 16, 121-132.
• TIKKIWAL, B. D. and TIKKIWAL, G. C., (1991). Sampling Strategies in Surveys. The Role of the Theory of T-Classes and Computers. Symposium Ind. Agri. Stat. Research Institute, New Delhi, 287-296.
• TIKKIWAL, G. C. and GUPTA, A. K., (1991). Estimation of Population Mean under Successive Sampling When Various Weights and Regression Coefficient are Unknown. Biometrical Journal, 33, 529-538.
• TIKKIWAL, G. C. and GHIYA, ALKA., (2000). A Generalized Class of Synthetic Estimators with Application to Crop Acreage Estimation for Small Domains. Biometrical Journal, 42 (7), 865-876.
• TIKKIWAL, G. C. and PANDEY, K. K., (2007). On Some Aspects of Small Area Estimation Using Auxiliary Information. Ph.D. Thesis under supervision of Prof. G. C. Tikkiwal, Head of Department of Mathematics and Statistics J. N. V. University Jodhpur Rajasthan.