On The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is UnknownOn The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is Unknown
Asian Journal of Probability and Statistics,
Page 235-250
DOI:
10.9734/ajpas/2021/v15i430377
Abstract
Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known population meanof auxiliary variable. In this paper, a new class of almost unbiased imputation method that uses as an estimate of is suggested. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.
Keywords:
- Estimators
- imputation scheme
- population mean
- study variable.
How to Cite
Audu, A., Danbaba, A., Ahmad, S. K., Musa, N., Shehu, A., Ndatsu, A. M., & Joseph, A. O. (2021). On The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is UnknownOn The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is Unknown. Asian Journal of Probability and Statistics, 15(4), 235-250. https://doi.org/10.9734/ajpas/2021/v15i430377
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Sahai A, Ray SK. And efficient estimator using auxiliary information, Metrika. 1980;27(4):271-275.
Srivastava Sk, Jhajj HA. A class of estimators of the population mean in survey sampling using auxiliary information Biometrika. 1981;68(1):341-343.
Ahmed A, Adewara AA, Singh RVK. Class of ratio estimators with known functions of auxiliary variable for estimating finite population variance. Asian Journal of Mathematics and Computer Research. 2016;12(1):63-70.
Audu A, Ishaq OO, Muili JO, Abubakar A, Rashida A, Akintola KA, Isah U. Modified estimators of population mean using robust multiple regression methods. NIPES Journal of Science and Technology Research. 2020;2(4):12–20.
Available:https://doi.org/10.37933/nipes/2.4.2020.2
Audu A, Adewara AA. Modified factor-type estimators under two-phase sampling. Punjab Journal of Mathematics. 2017;49(2):59-73. ISSN: 1016-2526.
Muili JO, Agwamba EN, Erinola YA, Yunusa MA, Audu A, Hamzat MA. Modified ratio-cum-product estimators of finite population variance. International Journal of Advances in Engineering and Management. 2020;2(4):309-319. DOI: 10.35629/5252-0204309319.
Zaman T. Generalized exponential estimators for the finite population mean. Statistics in Transition. New Series. 2020;21(1):159-168.
Zaman T, Kadilar C. Exponential ratio and product type estimators of the mean in stratified two-phase sampling. AIMS Mathematics. 2021;6(5):4265-4279.
Zaman T. An efficient exponential estimator of the mean under stratified random sampling. Mathematical Population Studies. 2021;8(2):104-121.
Yadav SK, Zaman T. Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators. Journal of Statistics and Management Systems; 2021.
DOI: 10.1080/09720510.2020.1864939
Ishaq OO, Audu A, Ibrahim A, Abdulkadir HS, Tukur K. On the linear combination of sample variance, ratio, and product estimators of finite population variance under two-stage sampling. Science Forum Journal of Pure and Applied Science. 2020;20:307-315.
DOI: http://dx.doi.org/10.5455/sf.90563
Audu A, Singh R, Khare S. Developing calibration estimators for population mean using robust measures of dispersion under stratified random. Statistics in Transition New Series. 2021;22(2):125–142.
DOI: 10.21307/stattrans-2021-019
Singh HP, Tailor R. Estimation of finite population mean with known coefficient of variation of an auxiliary character. Statistica. 2005;65(3):301-313.
Sisodia BVS, Dwivedi VK. Modified ratio estimator using coefficient of variation of auxiliary variable. Journal-Indian Society of Agricultural Statistics. 1981;33:13-18.
Khoshnevisan M, Singh R, Chauhan P, Sawan N, Smarandache F. A general family of estimators for estimating population means using known value of some population parameter(s). Far East Journal of Theoretical Statistics. 2007;22(2):181-191.
Singh R, Mishra P, Audu A, Khare S. Exponential type estimator for estimating finite population mean. Int. J. Comp. Theo. Stat. 2020;7(1):37-41.
Singh RVK, Audu A. Efficiency of ratio estimators in stratified random sampling using information on auxiliary attribute. International Journal of Engineering Science and Innovative Technology. 2013;2(1):166-172.
Ahmed A, Singh RVK, Adewara AA. Ratio and product type exponential estimators of population variance under transformed sample information of study and supplementary variables. Asian Journal of Mathematics and Computer Research. 2016;11(3):175-183.
Audu A, Yunusa MA, Ishaq OO, Lawal MK, Rashida A, Muhammad AH, et al. Difference-cum-ratio estimators for estimating finite population coefficient of variation in simple random sampling. Asian Journal of Probability and Statistics. 2021;13(3):13-29
Singh S. A new method of imputation in survey sampling. Statistics. 2009;43:499-511.
Barnard J, Meng XL. Applications of multiple imputation in medical studies: from AIDS to NHANES. Statistical Methods in Medical Research. 1999;8(1):17–36.
DOI:10.1177/096228029900800103
Gelman, Andrew, Jennifer Hill. Data analysis using regression and multilevel/ hierarchical models. Cambridge University Press. 2006;Ch.25.
Hansen MN, Hurwitz WN. The problem of non-response in sample surveys. Journal of the American Statistical Association. 1946;41:517–529.
Singh S, Horn S. Compromised imputation in survey sampling. Metrika. 2000; 51:267-276.
Singh S, Deo B. Imputation by power transformation. Statistical Papers. 2003;44:555-579.
Ahmed MS, Al-Titi Z, Al-Rawi Z, Abu-Dayyeh W. Estimation of a Population Mean using different Imputation Methods. Trans. 2006;7:1247-1264.
Wang L, Wang Q. Empirical likelihood for parametric model under imputation for missing data. Journal of Statistics and Management Systems.2006;9 (1):1-13.
Kadilar C, Cingi H. New ratio estimators using correlation coefficient. Interstat. 2006;4:1-11.
Toutenburg H, Srivastava VK, Shalabh A. Imputation versus imputation of missing values through ratio method in sample surveys. Statistical Papers. 2008;49.
Diana G, Perri PF. Improved estimators of the population mean for missing data. Communications in Statistics-Theory and Methods. 2010;39:3245–3251.
Al-Omari AI., Bouza CN, Herrera C. Imputation methods of missing data for estimating the population mean using simple random sampling with known correlation coefficient. Quality and Quantity. 2013;47: 353-365.
Singh GN, Maurya S, Khetan M, Kadilar C. Some imputation methods for missing data in sample surveys. Hacettepe Journal of Mathematics and Statistics. 2016;45(6):1865-1880.
Mishra P, Singh P, Singh R. A generalized class of estimators for estimating population mean using imputation technique. Journal of Reliability and Statistical Studies. 2017;10(2):33-41.
Singh BK, Gogoi U. Estimation of population mean using ratio cum product imputation techniques in sample survey. Res. Rev, J. Stat. 2018;7:38-49.
Singh AK, Singh P, Singh VK. Exponential-type compromised imputation in survey sampling. J. Stat. Appl. 2014;3(2):211-217.
Prasad S. A study on new methods of ratio exponential type imputation in sample surveys. Hacettepe Journal of Mathematics and Statistics; 2017. DOI: 10.15672/HJMS.2016.392.
Audu A., Ishaq OO, Isah U, Muhammed, S., Akintola, K. A., A. Rashida, A., and Abubakar. A. (2020) On the Class of Exponential-Type Imputation Estimators of Population Mean with Known Population Mean of Auxiliary Variable. NIPES Journal of Science and Technology Research 2(4) 2020 pp.1 - 11 pISSN-2682-5821, eISSN-2682-5821.
Audu A, Singh R, Khare S. New regression-type compromised imputation class of estimators with known parameters of auxiliary variable. Communications in statistics – Simulation and Computation. 2021;1-13.
DOI: 10.1080/03610918.2021.1970182
Audu A, Ishaq OO, Abubakar A, Akintola KA, Isah U, Rashida A, Muhammad S. Regression-type imputation class of estimators using auxiliary attribute. Asian Research Journal of Mathematics. 2021;17(5):1-13.
DOI: 10.9734/ARJOM/2021/v17i530296
Audu A, Ishaq OO, Muili J, Zakari Y, Ndatsu AM, Muhammed S. On the Efficiency of Imputation Estimators using Auxiliary Attribute. Continental J. Applied Sciences. 2020;15(1):1-13.
DOI: 10.5281/zenodo.3721046
Shahzad U, Al-Noor NH, Hanif M, Sajjad I, Muhammad Anas M. Imputation based mean estimators in case of missing data utilizing robust regression and variance–covariance matrices. Communications in Statistics-Simulation and Computation. 2020;1-20.
Audu A, Singh RVK. Exponential-type regression compromised imputation class of estimators. Journal of Statistics and Management Systems. 2021;24(6):1253-1266.
DOI: 10.1080/09720510.2020.1814501
Kalton G. The treatment of missing survey data. Survey Methodology. 1986;12: 1-6.
Lee H, Rancourt E, Sarndal CE. Experiments with variance estimation from survey data with imputed value. Journal of Official Statistics. 1994;10(3):231-243.
Sahai A, Ray SK. And efficient estimator using auxiliary information, Metrika. 1980;27(4):271-275.
Srivastava Sk, Jhajj HA. A class of estimators of the population mean in survey sampling using auxiliary information Biometrika. 1981;68(1):341-343.
Ahmed A, Adewara AA, Singh RVK. Class of ratio estimators with known functions of auxiliary variable for estimating finite population variance. Asian Journal of Mathematics and Computer Research. 2016;12(1):63-70.
Audu A, Ishaq OO, Muili JO, Abubakar A, Rashida A, Akintola KA, Isah U. Modified estimators of population mean using robust multiple regression methods. NIPES Journal of Science and Technology Research. 2020;2(4):12–20.
Available:https://doi.org/10.37933/nipes/2.4.2020.2
Audu A, Adewara AA. Modified factor-type estimators under two-phase sampling. Punjab Journal of Mathematics. 2017;49(2):59-73. ISSN: 1016-2526.
Muili JO, Agwamba EN, Erinola YA, Yunusa MA, Audu A, Hamzat MA. Modified ratio-cum-product estimators of finite population variance. International Journal of Advances in Engineering and Management. 2020;2(4):309-319. DOI: 10.35629/5252-0204309319.
Zaman T. Generalized exponential estimators for the finite population mean. Statistics in Transition. New Series. 2020;21(1):159-168.
Zaman T, Kadilar C. Exponential ratio and product type estimators of the mean in stratified two-phase sampling. AIMS Mathematics. 2021;6(5):4265-4279.
Zaman T. An efficient exponential estimator of the mean under stratified random sampling. Mathematical Population Studies. 2021;8(2):104-121.
Yadav SK, Zaman T. Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators. Journal of Statistics and Management Systems; 2021.
DOI: 10.1080/09720510.2020.1864939
Ishaq OO, Audu A, Ibrahim A, Abdulkadir HS, Tukur K. On the linear combination of sample variance, ratio, and product estimators of finite population variance under two-stage sampling. Science Forum Journal of Pure and Applied Science. 2020;20:307-315.
DOI: http://dx.doi.org/10.5455/sf.90563
Audu A, Singh R, Khare S. Developing calibration estimators for population mean using robust measures of dispersion under stratified random. Statistics in Transition New Series. 2021;22(2):125–142.
DOI: 10.21307/stattrans-2021-019
Singh HP, Tailor R. Estimation of finite population mean with known coefficient of variation of an auxiliary character. Statistica. 2005;65(3):301-313.
Sisodia BVS, Dwivedi VK. Modified ratio estimator using coefficient of variation of auxiliary variable. Journal-Indian Society of Agricultural Statistics. 1981;33:13-18.
Khoshnevisan M, Singh R, Chauhan P, Sawan N, Smarandache F. A general family of estimators for estimating population means using known value of some population parameter(s). Far East Journal of Theoretical Statistics. 2007;22(2):181-191.
Singh R, Mishra P, Audu A, Khare S. Exponential type estimator for estimating finite population mean. Int. J. Comp. Theo. Stat. 2020;7(1):37-41.
Singh RVK, Audu A. Efficiency of ratio estimators in stratified random sampling using information on auxiliary attribute. International Journal of Engineering Science and Innovative Technology. 2013;2(1):166-172.
Ahmed A, Singh RVK, Adewara AA. Ratio and product type exponential estimators of population variance under transformed sample information of study and supplementary variables. Asian Journal of Mathematics and Computer Research. 2016;11(3):175-183.
Audu A, Yunusa MA, Ishaq OO, Lawal MK, Rashida A, Muhammad AH, et al. Difference-cum-ratio estimators for estimating finite population coefficient of variation in simple random sampling. Asian Journal of Probability and Statistics. 2021;13(3):13-29
Singh S. A new method of imputation in survey sampling. Statistics. 2009;43:499-511.
Barnard J, Meng XL. Applications of multiple imputation in medical studies: from AIDS to NHANES. Statistical Methods in Medical Research. 1999;8(1):17–36.
DOI:10.1177/096228029900800103
Gelman, Andrew, Jennifer Hill. Data analysis using regression and multilevel/ hierarchical models. Cambridge University Press. 2006;Ch.25.
Hansen MN, Hurwitz WN. The problem of non-response in sample surveys. Journal of the American Statistical Association. 1946;41:517–529.
Singh S, Horn S. Compromised imputation in survey sampling. Metrika. 2000; 51:267-276.
Singh S, Deo B. Imputation by power transformation. Statistical Papers. 2003;44:555-579.
Ahmed MS, Al-Titi Z, Al-Rawi Z, Abu-Dayyeh W. Estimation of a Population Mean using different Imputation Methods. Trans. 2006;7:1247-1264.
Wang L, Wang Q. Empirical likelihood for parametric model under imputation for missing data. Journal of Statistics and Management Systems.2006;9 (1):1-13.
Kadilar C, Cingi H. New ratio estimators using correlation coefficient. Interstat. 2006;4:1-11.
Toutenburg H, Srivastava VK, Shalabh A. Imputation versus imputation of missing values through ratio method in sample surveys. Statistical Papers. 2008;49.
Diana G, Perri PF. Improved estimators of the population mean for missing data. Communications in Statistics-Theory and Methods. 2010;39:3245–3251.
Al-Omari AI., Bouza CN, Herrera C. Imputation methods of missing data for estimating the population mean using simple random sampling with known correlation coefficient. Quality and Quantity. 2013;47: 353-365.
Singh GN, Maurya S, Khetan M, Kadilar C. Some imputation methods for missing data in sample surveys. Hacettepe Journal of Mathematics and Statistics. 2016;45(6):1865-1880.
Mishra P, Singh P, Singh R. A generalized class of estimators for estimating population mean using imputation technique. Journal of Reliability and Statistical Studies. 2017;10(2):33-41.
Singh BK, Gogoi U. Estimation of population mean using ratio cum product imputation techniques in sample survey. Res. Rev, J. Stat. 2018;7:38-49.
Singh AK, Singh P, Singh VK. Exponential-type compromised imputation in survey sampling. J. Stat. Appl. 2014;3(2):211-217.
Prasad S. A study on new methods of ratio exponential type imputation in sample surveys. Hacettepe Journal of Mathematics and Statistics; 2017. DOI: 10.15672/HJMS.2016.392.
Audu A., Ishaq OO, Isah U, Muhammed, S., Akintola, K. A., A. Rashida, A., and Abubakar. A. (2020) On the Class of Exponential-Type Imputation Estimators of Population Mean with Known Population Mean of Auxiliary Variable. NIPES Journal of Science and Technology Research 2(4) 2020 pp.1 - 11 pISSN-2682-5821, eISSN-2682-5821.
Audu A, Singh R, Khare S. New regression-type compromised imputation class of estimators with known parameters of auxiliary variable. Communications in statistics – Simulation and Computation. 2021;1-13.
DOI: 10.1080/03610918.2021.1970182
Audu A, Ishaq OO, Abubakar A, Akintola KA, Isah U, Rashida A, Muhammad S. Regression-type imputation class of estimators using auxiliary attribute. Asian Research Journal of Mathematics. 2021;17(5):1-13.
DOI: 10.9734/ARJOM/2021/v17i530296
Audu A, Ishaq OO, Muili J, Zakari Y, Ndatsu AM, Muhammed S. On the Efficiency of Imputation Estimators using Auxiliary Attribute. Continental J. Applied Sciences. 2020;15(1):1-13.
DOI: 10.5281/zenodo.3721046
Shahzad U, Al-Noor NH, Hanif M, Sajjad I, Muhammad Anas M. Imputation based mean estimators in case of missing data utilizing robust regression and variance–covariance matrices. Communications in Statistics-Simulation and Computation. 2020;1-20.
Audu A, Singh RVK. Exponential-type regression compromised imputation class of estimators. Journal of Statistics and Management Systems. 2021;24(6):1253-1266.
DOI: 10.1080/09720510.2020.1814501
Kalton G. The treatment of missing survey data. Survey Methodology. 1986;12: 1-6.
Lee H, Rancourt E, Sarndal CE. Experiments with variance estimation from survey data with imputed value. Journal of Official Statistics. 1994;10(3):231-243.
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