基于Score检验统计的粗差探测法
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摘要
针对观测数据同时含有粗差和系统误差时粗差难以探测的问题,本文将粗差纳入随机模型,提出了一种基于Score检验统计的粗差探测方法。首先构造半参数模型的惩罚极大似然函数,给出了相应的解的表达式。然后构造Score检验统计量,推导出具体表达式,给出了相应的粗差探测步骤。最后,用一组含有粗差的模拟数据验证了本文算法的有效性。
It is difficult to detect gross errors when there are both gross errors and systematic errors in the observed data. In this paper,the gross errors are included in the stochastic model,and a method of gross errors detection based on Score test statistics is proposed. Firstly,the penalty maximum likelihood function of the semi-parametric model is constructed,and the expression of the corresponding solution is given. Then the Score test statistics are constructed,the concrete expressions are derived,and the corresponding gross error detection steps are given. Finally,a set of simulation data with gross errors are used to verify the effectiveness of the proposed algorithm.
It is difficult to detect gross errors when there are both gross errors and systematic errors in the observed data. In this paper,the gross errors are included in the stochastic model,and a method of gross errors detection based on Score test statistics is proposed. Firstly,the penalty maximum likelihood function of the semi-parametric model is constructed,and the expression of the corresponding solution is given. Then the Score test statistics are constructed,the concrete expressions are derived,and the corresponding gross error detection steps are given. Finally,a set of simulation data with gross errors are used to verify the effectiveness of the proposed algorithm.
引文
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[2]金丽宏,吕玉婷,汪耀,等.基于部分最小二乘岭估计的粗差定值定位[J].测绘工程,2016,25(6):61-64.
[3]王延停,归庆明,张倩倩.基于Kullback-Leiber距离粗差探测的Bayes方法[J].大地测量与地球动力学,2012,32(2):51-55.
[4]陈轲,归庆明,柳丽,等. Gauss-Markov模型的t型抗差估计[J].测绘学报,2008,37(3):280-284.
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[6]杨元喜.参数M估计及验后精度综述[J].测绘通报,1991(8):6-10.
[7]朱仲义.系统分析中半参数非线性模型的统计分析[D].南京:东南大学,1999.
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[9]丁士俊.测量数据的建模与半参数估计[D].武汉:武汉大学,2005.
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