Optimal variance estimation for generalized regression predictor |
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| Institution: | 1. Computer Science Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700035, India;2. Department of Statistics, Presidency College, Calcutta 700073, India;1. Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan;2. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan;3. Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan;4. Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;5. School of Mathematics and Statistics, Central South University, Changsha, China;6. Department of Statistics, University of Wah at Wah Cantt, Quaid Avenue, Wah Cantt, Pakistan;1. Department of Statistics, University of Lucknow, Lucknow, U.P. 226007, India;2. Department of Statistics, Amity University, Lucknow, U.P. 226028, India;3. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia;1. School of Economics and Management, Taiyuan Normal University, Jinzhong 030619, China;2. Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan;3. Department of Mathematics and Statistics, Institute of Southern Punjab, Pakistan;4. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia;5. Mathematics Department, Faculty of Science, Al-Baha University, Saudi Arabia;6. Department of Statisitcs, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia;7. Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt;8. School of Finance and Economics, Jiangsu University, Zhenjiang 212013, China |
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| Abstract: | The generalized regression (greg) predictor for the finite population total of a real variable is often employed when values of an auxiliary variable are available. Several variance estimators for it do well in large samples though bearing no optimality properties. We find a variance estimator which, under a restrictive model, has an optimality property under ‘exact’ as well as ‘asymptotic’ analysis. But this involves model parameters. Under a further restriction on the model, two model-parameter-free variance estimators are derived sharing the same ‘asymptotic’ optimality. Numerical illustrations through simulation are presented to demonstrate marginal improvements in using them rather than their predecessors. Two of the latter, though not optimal, are simpler, intuitively appealing, compete well in large samples, generally applicable and should be persisted with in practice. |
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