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| CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE | |
| 引用本文： | SONGWeixing CHENGPing. CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE[J]. 系统科学与复杂性, 2002, 15(3): 315-328 |
| 作者姓名： | SONGWeixing CHENGPing |
| 作者单位： | SONG Weixing (Department of Mathematics，Beijing Normal University，Beijing 100875，China)CHENG Ping(Systems Science Institute，Academy of Mathematics and Systems Science，Chinese Academy of Sciences，Beijing 100080，China) |
| 基金项目： | This research is supported by Youth Science Foundation of Beijing Normal University. |
| 摘 要： | In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family. |
| 关 键 词： | 系统分析 效率理论 褶积理论 渐近效率 两侧截平分布族 |
CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY--THE NORMAL CASE |
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| SONG Weixing. CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY--THE NORMAL CASE[J]. Journal of Systems Science and Complexity, 2002, 15(3): 315-328 | |
| Authors: | SONG Weixing |
| Abstract: | In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family. |
| Keywords: | Two-side truncated distribution family local asymptotic equivariant estimate convolution theorem asymptotic efficiency. |
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