Study of general families of estimators in two-stage sampling with unequal size clusters under non-response

Abstract

This paper presents some salient features of the biased and unbiased estimators of population mean in two-stage sampling with unequal size
clusters in presence of non-response. Paper proposes general families of factor-type estimators of population mean using information on an
auxiliary variable under the condition that the non-response is observed on study variable only and on both study and auxiliary variables respectively. Biases and mean square errors of the families are obtained. Optimum estimators of the proposed families have been investigated in both the cases. An empirical study is also carried out to support the theoretical results.

Keywords

• Two-stage sampling,unequal size clusters,auxiliary information,factor-type estimators,non-response

References

1. Ahmed, M.S. Some estimators for a nite population mean under two-stage sampling using multivariate auxiliary information, Applied Mathematics and Computation, 153(2), 505-511, 2004.
2. Bellhouse, D. R. and Rao, J. N. K. On the eciency of prediction estimator in two-stage sampling, Journal of Statistical Planning and Inference, 13, 269-281, 1986.
3. Chaudhary, M. K. and Singh, V. K. Estimating the population mean in two-stage sampling with equal size clusters under non-response using auxiliary characteristic, Mathematical Journal of Interdisciplinary Sciences, 2(1), 43-55, 2013.
4. Eideh, A. and Nathan, G. Two-stage informative cluster sampling-estimation and predic- tion with applications for small-area models, Journal of Statistical Planning and Inference, 139(9), 3088-3101, 2009.
5. Hansen, M. H. and Hurwitz, W. N. The problem of non-response in sample surveys, Journal of the American Statistical Association, 41, 517-529, 1946.
6. Khan, A. and Muttlak, H. A. Adjusted two-stage adaptive cluster sampling, Applied Math- ematics and Computation, 126(1), 83-95, 2002.
7. Sahoo, L. N., Das, B. C. and Sahoo, J. A class of predictive estimators in two stage sampling, Journal of the Indian Society of Agricultural Statistics, 63(2), 175-180, 2009.
8. Sahoo, L. N. and Panda, P. A class of estimators in two-stage sampling with varying prob- abilities, South African Statistical journal, 31, 151-160, 1997.

9. Sarndal, C. E., Swensson, B. and Wretman, J. Model Assisted Survey Sampling, Springer- Verlag, New York, Inc. Appendix D, 662, 1992.
10. Singh, V. K. and Shukla, D. One parameter family of factor-type ratio estimators, Metron,45(1-2), 273-283, 1997.