The global minimum variance unbiased estimator of the parameter for a truncated parameter family under the optimal ranked set sampling |
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Authors: | Wangxue Chen Yi Tian Minyu Xie |
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Affiliation: | 1. Department of Mathematics and Statistics, Jishou University, Jishou, People’s Republic of China;2. Department of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China |
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Abstract: | The minimum variance unbiased estimators (MVUEs) of the parameters for various distributions are extensively studied under ranked set sampling (RSS). However, the results in existing literatures are only locally MVUEs, i.e. the MVUE in a class of some unbiased estimators is obtained. In this paper, the global MVUE of the parameter in a truncated parameter family is obtained, that is to say, it is the MVUE in the class of all unbiased estimators. Firstly we find the optimal RSS according to the character of a truncated parameter family, i.e. arrange RSS based on complete and sufficient statistics of independent and identically distributed samples. Then under this RSS, the global MVUE of the parameter in a truncated parameter family is found. Numerical simulations for some usual distributions in this family fully support the result from the above two-step optimizations. A real data set is used for illustration. |
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Keywords: | Ranked set sampling complete sufficient statistic truncation parameter family minimum variance unbiased estimator |
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