The probability of type I and type II errors in imprecise hypothesis testing with an application to geodetic deformation analysis
The probability of type I and type II errors in imprecise hypothesis testing with an application to geodetic deformation analysis
复制标题
不精确假设检验中 I 类和 II 类错误的概率及其在大地变形分析中的应用
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
H. Kutterer
中科院分区：
文献类型：
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作者：
I. Neumann;H. Kutterer
在许多工程学科中，感兴趣的模型参数是通过最小二乘平差从大量异质和冗余观测值中估计的。在统计假设检验中检查模型参数的显著性、离群值检测和模型选择本身。假设的接受和拒绝与两类错误密切相关。如果零假设被拒绝，则发生I类错误，尽管它是真的。如果零假设被接受，则发生II类错误，尽管它是假的。本文给出了线性参数估计中假设检验的一般方法，当不确定性考虑到随机变异性和区间/模糊误差时。研究重点是I型和II型错误的概率。应用程序的概述详细示出理论和数值例子的参数化的大地测量监测网（变形分析）。
In many engineering disciplines the interesting model parameters are estimated from a large number of heterogeneous and redundant observations by a least-squares adjustment. The significance of the model parameters, outlier detection and the model selection itself are checked within statistical hypothesis tests. The acceptance and the rejection of the hypothesis are strongly related with two types of errors. A type I error occurs if the null hypothesis is rejected, although it is true. A type II error occurs if the null hypothesis is accepted, although it is false. This paper proposes a general procedure to hypothesis testing in linear parameter estimation, if the uncertainty is considered by random variability and interval/fuzzy errors. The study focuses on the probability of type I and type II errors. The applied procedure is outlined in detail showing both theory and numerical examples for the parameterisation of a geodetic monitoring network (deformation analysis).