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Maximum Likelihood and the Maximum Product of Spacings from the Viewpoint of the Method of Weighted Residuals
https://doi.org/10.24517/00062413
https://doi.org/10.24517/00062413d8ab68a1-cdba-4e68-b19a-9a243dc75a99
| 名前 / ファイル | ライセンス | アクション |
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SC-PR-KAWANISHI-T-2020-156.pdf (268.3 kB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||||
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| 公開日 | 2021-06-10 | |||||||
| タイトル | ||||||||
| タイトル | Maximum Likelihood and the Maximum Product of Spacings from the Viewpoint of the Method of Weighted Residuals | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | journal article | |||||||
| ID登録 | ||||||||
| ID登録 | 10.24517/00062413 | |||||||
| ID登録タイプ | JaLC | |||||||
| 著者 |
Kawanishi, Takuya
× Kawanishi, Takuya |
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| 著者別表示 |
川西, 琢也
× 川西, 琢也
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| 提供者所属 | ||||||||
| 内容記述タイプ | Other | |||||||
| 内容記述 | 金沢大学理工研究域フロンティア工学系 | |||||||
| 書誌情報 |
Computational and Applied Mathematics 巻 39, 号 3, p. 156, 発行日 2020-05-29 |
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| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 0101-8205 | |||||||
| ISSN | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 1807-0302 | |||||||
| 出版者 | ||||||||
| 出版者 | Springer | |||||||
| 抄録 | ||||||||
| 内容記述タイプ | Abstract | |||||||
| 内容記述 | In parameter estimation, the maximum-likelihood method (ML) does not work for some distributions. In such cases, the maximum product of spacings method (MPS) is used as an alternative. However, the advantages and disadvantages of the MPS, its variants, and the ML are still unclear. These methods are based on the Kullback–Leibler divergence (KLD), and we consider applying the method of weighted residuals (MWR) to it. We prove that, after transforming the KLD to the integral over [0, 1], the application of the collocation method yields the ML, and that of the Galerkin method yields the MPS and Jiang’s modified MPS (JMMPS); and the application of zero boundary conditions yields the ML and JMMPS, and that of non-zero boundary conditions yields the MPS. Additionally, we establish formulas for the approximate difference among the ML, MPS, and JMMPS estimators. Our simulation for seven distributions demonstrates that, for zero boundary condition parameters, for the bias convergence rate, ML and JMMPS are better than the MPS; however, regarding the MSE for small samples, the relative performance of the methods differs according to the distributions and parameters. For non-zero boundary condition parameters, the MPS outperforms the other methods: the MPS yields an unbiased estimator and the smallest MSE among the methods. We demonstrate that from the viewpoint of the MWR, the counterpart of the ML is JMMPS not the MPS. Using this KLD-MWR approach, we introduce a unified view for comparing estimators, and provide a new tool for analyzing and selecting estimators. © 2020, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional. | |||||||
| 著者版フラグ | ||||||||
| 出版タイプ | AM | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||
| 関連URI | ||||||||
| 識別子タイプ | URI | |||||||
| 関連識別子 | http://link.springer.com/journal/40314 | |||||||
| 関連名称 | http://link.springer.com/journal/40314 | |||||||
| 関連URI | ||||||||
| 識別子タイプ | URI | |||||||
| 関連識別子 | https://link.springer.com/article/10.1007/s40314-020-01179-7 | |||||||
| 関連名称 | https://link.springer.com/article/10.1007/s40314-020-01179-7 | |||||||
| 関連URI | ||||||||
| 識別子タイプ | URI | |||||||
| 関連識別子 | https://link.springer.com/journal/40314/volumes-and-issues/39-3?page=2 | |||||||
| 関連名称 | https://link.springer.com/journal/40314/volumes-and-issues/39-3?page=2 | |||||||
