The asymptotic variance-covariance matrix, Baarda test and the reliability of L-1-norm estimates
文献类型：期刊论文
| 作者 | Junhuan, P |
| 刊名 | JOURNAL OF GEODESY
 |
| 出版日期 | 2005-05-01 |
| 卷号 | 78期号:11-12页码:668-682 |
| 关键词 | L-1-norm estimate modified L-1-norm estimate Bahadur-type linear representation asymptotic variance covariance matrix Baarda test statistic reliability outliers/gross errors leverage points robust estimation |
| 英文摘要 | This paper derives the complete Bahadur-type linear representation of the basic vector including the residual vector and the adjusted vector of the observations for the L-1-norm estimation. The asymptotic variance-covariance matrix of the basic vector is obtained accordingly. The L-1-Baarda test statistic is successfully obtained from the residual and its variance. The reliability, understood as the ability to detect as well as resist outliers, of the L-1 -norm estimate is discussed for the L-1-Baarda test statistic, as compared with the reliability of the L-2-norm estimate; it is less affected by the variation of the redundancy component. According to the relationship between residuals and true errors for the L-1 norm estimate, the outlier is almost completely projected onto the corresponding residual. This is why the L-1-Baarda test seems to locate outliers more correctly. For the L-2 -norm estimates, the outlier is partly projected onto the corresponding residual at the proportion of the corresponding redundancy component, which may easily result in an error of the third kind - the mis-location of the outlier through the L-2-Baarda test. Besides, the robustness of the L-1-norm estimate is no longer guaranteed if there exist leverage points in observations. This paper suggests the modified L-1-norm estimate for robust estimation of leverage points, and derives its Bahadur-type representation and the corresponding variance-covariance matrix. In numerical examples, the L-1-norm estimate and modified L-1-norm estimate are compared with the L-2-norm estimate, Biber-estimate, Koch's method and the least median of squares method. The result shows that the L-1-norm estimation can better identify small outliers, and that the modified L-1-norm estimate is valid for robust estimation in the presence of leverage points. |
| WOS标题词 | Science & Technology ; Physical Sciences ; Technology |
| 类目[WOS] | Geochemistry & Geophysics ; Remote Sensing |
| 研究领域[WOS] | Geochemistry & Geophysics ; Remote Sensing |
| 关键词[WOS] | OUTLIER DETECTION ; LINEAR-MODELS ; REGRESSION |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000229856700004 |
| 源URL | [http://119.78.226.72/handle/331011/19372]  |
| 专题 | 上海天文台_天文地球动力学研究中心 |
| 作者单位 | 1.Chongqing Univ, Sch Civil Engn, Chongqing 400044, Peoples R China 2.CAS, Shanghai Astron Observ, Shanghai 200030, Peoples R China |
| 推荐引用方式 GB/T 7714 | Junhuan, P. The asymptotic variance-covariance matrix, Baarda test and the reliability of L-1-norm estimates[J]. JOURNAL OF GEODESY,2005,78(11-12):668-682. |
| APA | Junhuan, P.(2005).The asymptotic variance-covariance matrix, Baarda test and the reliability of L-1-norm estimates.JOURNAL OF GEODESY,78(11-12),668-682. |
| MLA | Junhuan, P."The asymptotic variance-covariance matrix, Baarda test and the reliability of L-1-norm estimates".JOURNAL OF GEODESY 78.11-12(2005):668-682. |
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来源：上海天文台
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