引用本文: 潘雄, 吕玉婷, 汪耀, 罗静, 徐景田. 基于半参数平差模型的粗差定位与定值研究[J]. 武汉大学学报 ( 信息科学版), 2016, 41(11): 1421-1426.
PAN Xiong, LV Yuting, WANG Yao, LUO Jing, XU Jingtian. Research of the Location and Valuation of Gross Error Based on Semi-parametric Adjustment Model[J]. Geomatics and Information Science of Wuhan University, 2016, 41(11): 1421-1426.
 Citation: PAN Xiong, LV Yuting, WANG Yao, LUO Jing, XU Jingtian. Research of the Location and Valuation of Gross Error Based on Semi-parametric Adjustment Model[J]. Geomatics and Information Science of Wuhan University, 2016, 41(11): 1421-1426.

## Research of the Location and Valuation of Gross Error Based on Semi-parametric Adjustment Model

• 摘要: 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 QC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。

Abstract: For observational data with systematic and gross errors, this paper presents a method to locate and value gross errors by introducing the mixed Cook distance into the semiparametric model. Firstly, by structuring a penalized least squares function and using Taylor expansion, and according to the equivalence of the mean shift model and data deleted model, the penalized least squares estimation expression of the parametric and non-parametric components are obtained for the data with a deleted ith observation, which is useful for locating the gross errors. Secondly, with the help of mixed Cook distance as a kind of diagnostic statistic, the corresponding formula for the parametric and non-parametric components are deducted, in order to improve the accuracy when locating gross errors. Common forms of parameters Q and C are given, which can influence the mixed Cook distance directly, as different choices for the parameters yield different results. By selecting the appropriate parameters and calculating the Cook distances of the parametric and non-parametric components, the positions of gross errors are determined, thus the systematic error and gross error can be separated from the observed data. Using simulated computations and a real example, it is shown that the method can effectively determine the position and fixed values of gross error, and illustrating the effectiveness of the proposed approach.

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