|
|
- 2016
基于半参数平差模型的粗差定位与定值研究
|
Abstract:
对于包含系统误差和粗差的观测数据，本文将混合Cook距离引入到半参数模型中，实现了粗差的定值定位。首先，构造补偿最小二乘函数，利用泰勒展式，根据均值漂移模型与删失模型的等价性，导出了观测数据中剔除第i个观测数据前后参数分量和非参数分量相应估计值之间的关系式，为粗差的定位分析奠定了基础。其次，将混合Cook距离作为诊断统计量，进行粗差定位分析，得到了参数分量和非参数分量的诊断统计量的简洁计算公式，为了提高粗差定位的准确性，给出了混合Cook距离参数Q和C的一些常用形式，通过合理选择相应参数，计算参数分量和非参数分量的距离函数，实现粗差的定位，并将系统误差和粗差从观测数据中区别开来。最后通过模拟算例和实测数据验证了本文方法的正确性
| [1] | Yu Zongchou,Li Mingfeng. A Further Discussion on the Nature of the LEGE Method and Its Improved Seaching Method[J]. Journal of Wuhan Technical University of Surveying and Mapping,1998,23(3):238-243(於宗俦,李明峰. 对LEGE法性质的进一步讨论及其改进搜索方法[J]. 武汉测绘科技大学学报,1998,23(3):238-243) |
| [2] | Zhang Zhenglu,Zhang Songlin,Luo Nianxue,et al. Algorithm of Simultaneous Location and Evaluation of Multi-Dimensional Gross Errors and Its Implementation[J]. Geomatics and Information Science of Wuhan University,2003,28(4):400-404(张正禄,张松林,罗年学,等. 多维粗差定位与定值的算法研究[J]. 武汉大学学报·信息科学版,2003,28(4):400-404) |
| [3] | H？ggstr？m J. Bandwidth Selection for Backfitting Estimation of Semiparametric Additive Models:A Simulation Study[J]. Computational Statistics and Data Analysis, 2013,62:136-148 |
| [4] | Pan Xiong,Sun Haiyan. Semiparametric p-norm Maximum Likeli Hood Regression[J]. Acta Geodaetica et Cartographica Sinica,2005,34(1):30-34. (潘雄,孙海燕. 半参数p-范极大似然回归[J]. 测绘学报,2005,34(1):30-34) |
| [5] | Ruppert D,Wand M P,Caroll R J. Semiparametric Regression[M]. Cambridge:Cambridge University Press,2003. |
| [6] | Song Lijie,Yang Yuanxi. Comparison Between Data Snooping and LEGE[J]. Acta Geodaetica et Cartographica Sinica,1999,28(4):295-300(宋力杰,杨元喜. 均值漂移粗差探测法与LEGE的比较[J]. 测绘学报,1999,28(4):295-300) |
| [7] | Cook R D.Weisberg S. Residual and Influence in Regression[M]. New York:Chapman and Hall, 1982 |
| [8] | Wang Haitao,Ou Jikun,Yuan Yunbin,et al. On Equivalence of Three Estimators for Outliers in Linear Model[J]. Geomatics and Information Science of Wuhan University,2013,38(2):162-166(王海涛,欧吉坤,袁运斌,等. 估计观测值粗差三种方法的等价性讨论[J]. 武汉大学学报·信息科学版,2013,38(2):162-166) |
| [9] | Zhu Zhongyi,Wei Bocheng. Diagnostic and Influence Analysis for Semiparametric Nonlinear Model[J]. Acta Mathematicae Applicatae Sinica,2001,24(4):568-581(朱仲义,韦博成. 半参数非线性模型的统计诊断与影响分析[J]. 应用数学学报,2001,24(4):568-581) |
| [10] | Zeng Linrui. Some Studies on the Semiparametric Generalized Linear Model[D]. Shanghai:East China Normal University, 2004(曾林蕊. 半参数广义线性模型若干问题的研究[D]. 上海:华东师范大学,2004) |
| [11] | Gui Qingming, Li Xiaolo, Gong Y. A Bayesian Unmasking Method for Locating Multiple Gross Errors Based on Posterior Probabilities of Classification Variables[J].Journal of Geodesy, 2011, 85(4):191-203 |
| [12] | Ou Jikun. Quasi-accurate Detection of Gross Errors (QUAD)[J].Acta Geodaetica et Cartographica Sinica,1999,28(1):15-20(欧吉坤. 粗差的拟准检定方法(QUAD法)[J].测绘学报,1999,28(1):15-20) |
| [13] | Sun Haiyan,Pan Xiong. The Statistical Property of Semiparametric Estimators with Positively Definite Regular Matrix[J]. Acta Geodaetica et Cartographica Sinica,2004,33(3):228-232(孙海燕,潘雄. 正规化矩阵正定时半参数估计量的统计性质[J]. 测绘学报,2004,33(3):228-232) |
| [14] | Pan Xiong. Theory and Application Research in Semiparametric Model[D]. Wuhan:Wuhan University, 2005(潘雄.半参数模型的估计理论及应用[D]. 武汉:武汉大学,2005 |
