Estimation of Population Total in the Presence of Missing Values Using a Modified Murthy's Estimator and the Weight Adjustment Technique

Oyoo David Odhiambo¹ and Christopher Ouma Onyango^1,

¹Department of Statistics and Actuarial Science, Kenyatta University-Kenya

Cite this paper

Oyoo David Odhiambo and Christopher Ouma Onyango. Estimation of Population Total in the Presence of Missing Values Using a Modified Murthy's Estimator and the Weight Adjustment Technique. American Journal of Applied Mathematics and Statistics. 2014; 2(3):163-167. doi: 10.12691/AJAMS-2-3-12

Abstract

Use of Murthy’s method in estimation of population parameters, such as population totals, population means, and population variances has been limited to surveys where survey data values are complete. This study applies weight adjustment technique to estimate a population total under simple random sampling without replacement. The asymptotic properties show that the estimated population total is sufficient for the true population total. The proposed estimator is obtained by symmetrizing Murthy’s estimator.

Keywords

Murthy’s estimator, missing values, weight adjustment

Copyright

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References

[1]	Brick, J.M. and Kalton, G. (1996) Handling missing data in survey research. Statistical Methods in Medical Research, 5, 215-238.
[2]	Broemeling, D. L. (2009). Bayesian Methods for Measures of Agreement (Chapman & Hall/CRC Biostatistics Series). Chapman and Hall/CRC Press.
[3]	Cochran, W. G. (1977). Sampling Techniques. 3rd Edition. New York, John Wiley.
[4]	Chang, C. and Ferry, B. (2012). Weighting Methods in Survey Sampling. Section on Survey Research Methods-JSM, 4768-4782.
[5]	Daroga, S. and Chaudhary, F. (2002). Theory and Analysis of Sample Survey Designs. New Delhi: New Age International (P) Limited Publishers.
[6]	Murthy, M. N. (1957). Ordered and unordered estimators in sampling without replacement. Sankhya, 18, 379-390.
[7]	Ouma, C., Odhiambo, R. and Orwa, G. (2010). Bootstrapping in Model-Based Estimation of a Finite Population Total Under Two-Stage Cluster Sampling With Unequal Cluster Sizes. Annals of Statistics, July Issue, 171-184.
[8]	Salehi, M. and Seber, G. A. (2002). Theory & Methods: A New Proof of Murthy's Estimator which Applies to Sequential Sampling. Australian & AMP New Zealand Journal of Statistics, 43(3), 281-286.
[9]	Shahbaz, Q. M., and Ayesha, S. (2008). A new symmetrized estimator of population total in unequal probability sampling. Journal of Statistics, 13(1), 20-25.
[10]	Singh, H. P. and Solanki, R. S. (2012). An alternative procedure for estimating the population mean in simple random sampling. Pakistan Journal of Statistics and Operation Research, 8(2), N 1816-2711.