Homogeneous imputation under two phase probability proportional to size sampling

Abstract

In this paper, we consider the problem of missing complete at random (MCAR) values in two phase probability proportional to size ($ pps $) sampling for the estimation of population mean.  A class of estimators is considered by the suitable use of auxiliary information with the traditional estimators for imputing the missing values. Theoretically, bias and mean squared errors of the proposed estimators are obtained up to the first order approximation. Two numerical studies are carried out for relative comparison of the proposed estimators with mean estimator under two phase $pps$ sampling for each situation.

Keywords

• missing values,two phase sampling,imputation,probability proportional to size,auxiliary information

References

1. [1] M. Ahmed, O. Al-Titi, Z. Al-Rawi and W. Abu-Dayyeh, Estimation of a population mean using different imputation methods , Statistics in Transition 7(6): 1247-1264, 2006.
2. [2] D. F. Heitjan and S. Basu, Distinguishing missing at random and missing completely at random, The Amer. Stat. 50 (3), 207-213, 1996.
3. [3] C. N. B. Herrera and A. I. Al-Omari, Ranked set estimation with imputation of the missing observations: the median estimator, Rev. Invest. Opera. 32 (1), 30-37, 2011.
4. [4] J. K. Kim, A. Navarro and W. A. Fuller, Replication variance estimation for two- phase stratified sampling, J. Amer. Statist. Assoc. 101 (473), 312-320, 2006.
5. [5] R. J. Little and D. B. Rubin, Statistical analysis with missing data, John Wiley and Sons, 2014.
6. [6] C. Mohamed , S. A. Sedory and S. Singh, Imputation using higher order moments of an auxiliary variable, Comm. Statist. Simulation Comput. 46 (8), 6588-6617, 2017.
7. [7] M. N. Murthy, Sampling theory and methods, Stat. Pub. Soc. 204/1, Barrackpore Tunk Road Calcutta, India, 1976.
8. [8] J. N. Rao and R. Sitter, Variance estimation under two-phase sampling with applica- tion to imputation for missing data, Biometrika 82 (2), 453-460, 1995.

9. [9] D. B. Rubin, Inference and missing data, Biometrika 63 (3), 581-592, 1976.
10. [10] J. Shabbir and S. Gupta, Estimation of the finite population mean in two phase sampling when auxiliary variables are attributes, Hacet. J. Math. Stat. 39 (1), 121-129, 2010.
11. [11] H. P. Singh and S. Kumar, Estimation of mean in presence of non-response using two phase sampling scheme, Statist. Papers 51 (3), 559-582, 2010.
12. [12] H. P. Singh, S. Kumar and M. Kozak, Improved estimation of finite population mean using sub-sampling to deal with non response in two-phase sampling scheme, Comm. Statist. Theory Methods 39 (5), 791-802, 2010.
13. [13] M. U. Sohail, J. Shabbir and S. Ahmed, Modified class of ratio and regression type estimators for imputing scrambling response, Pakistan J. Statist., 33 (4), 277-300, 2017.
14. [14] S. Singh, Advanced Sampling Theory With Applications: How Michael Selected Amy, Volume 2. Springer Science and Business Media, 2003.