The Comparison of Mean Estimator by Imputation Methods under the Different Mechanisms of Missing Data
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Abstract
The purpose of this research was to compare the different imputation methods including Gira’s method, Singh's method, and Aliyu's method under the missing data mechanisms. There were three types of missing data mechanisms for estimation of the mean values: missing completely at random, missing at random, and missing not at random. In this study, the data was conducted through 10,000 simulations. The sample sizes were set at 30, 100, and 400 for a variety of missing data scenarios. The percentages of missing data were 5, 10 and 15. The criteria used for comparison were the mean squared error and the percentage of relative efficiency. From the results, it was found that the appropriate methods for estimating the mean values were Singh’s method, Aliyu’s method, and Gira’s method, respectively.
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References
Gibson, N. M., & Olejnik, S. (2003). Treatment of missing data at the second level of hierarchical linear models. Educational and Psychological Measurement, 63(2), 204-238.
วราฤทธิ์ พานิชกิจโกศลกุล. (2552). การจำลองแบบมอนติคาร์โลสำหรับประมาณค่าความแปรปรวนของการแจกแจงอินเวอร์สเกาส์เซียน เมื่อข้อมูลมีค่าสูญหาย, ว.การวิจัยกาสะลองคำ, 3(1), 14-23.
Chakrabarty, R. P. (1979). Some ratio estimators. Journal of the Indian Society of Agricultural Statistics, 31(1), 49-57.
Srivenkataramana T., & Tracy D. S. (1980). An alternative to ratio method in sample survey. Annals of the Institute of Statistical Mathematics, 32, 111-120.
Singh, V. K., & Shukla, D. (1987). One parameter family of factor-type ratio estimation. Metron, 45, 273-283.
Bahl, S., & Tuteja, R. K. (1991). Ratio and product type exponential estimator. Information and Optimization Sciences, 12(1), 159-163.
Singh, H. P., & Tailor, R. (2003). Use of known correlation coefficient in estimating the finite population means. Statistics in Transition, 6(4), 555-560.
Kadilar, C., & Cingi, H. (2006a). An improvement in estimating the population mean by using the correlation coefficient. Hacettepe Journal of Mathematics and Statistics, 35(1), 103-109.
Kadilar, C., & Cingi, H. (2006b). Improvement in estimating the population mean in simple random sampling. Applied Mathematics Letters, 19, 75-79.
Upadhyaya, L. N., Singh, H. P., Chatterjee, S., & Yadav, R. (2011). Improved ratio and product exponential type estimators. Journal of Statistical Theory and Practice, 5(2), 285-302.
Yadav, S. K., & Kadilar, C. (2013). Efficient family of exponential estimators for the population mean. Hacettepe Journal of Mathematics and Statistics, 42(6), 671-677.
Khan, S. A., Ali, H., Manzoor, S., & Alamgir, K. (2015). A class of transformed efficient ratio estimators of finite population mean. Pakistan Journal of Statistics, 31(4), 353-362.
Kadilar, G. O. (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15(2), 207-214.
Gira, A. A. (2015). Estimation of population mean with a new imputation method. Applied Mathematical Sciences, 9(34), 1663-1672.
Singh, R., Verma, H. K., & Sharma, P. (2016). Estimation of population mean using exponential type imputation technique for missing observations. Journal of Modern Applied Statistical Methods, 15(1), 358-372.
Aliyu, Y. H., Adewara, A. A., Audu, A., Abidoye, O. A., Sulaiman, I., & Aliyu, M. B. (2022). Modified compromized type method of imputation for estimating population mean. Journal of Scientific Research, 66(1), 404-410.
Little, R., & Rubin, D. (2002). Statistical analysis with missing data. New York: Wiley.
Vongprasert, J. (2021). Missing Data Imputation Based on Accuracy of Binary Classification. The Journal of King Mongkut's University of Technology North Bangkok, 31(1), 90-98.
Chodjuntug, K., & Lawson, N. (2020). A chain ratio exponential-type compromised imputation for mean estimation: case study on ozone pollution in Saraburi, Thailand. Journal of Probability and Statistics, 1, 1-6.
Chodjuntug, K., & Lawson, N. (2022). Imputation for estimating the population mean in the presence of nonresponse, with application to fine particle density in Bangkok. Mathematical Population Studies, [Online], available from : https://doi.org/10.1080/08898480.2021.1997466