以平面坐标变换为例的非线性模型的假设检验

IF 0.9 Q4 REMOTE SENSING
R. Lehmann, M. Lösler
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引用次数: 5

摘要

在大地测量学中,假设检验应用于广泛的应用领域,例如异常值检测,变形分析或更普遍的模型优化。由于一个决策可能产生深远的影响,因此需要这种假设检验具有较高的统计检验能力。内曼-皮尔逊引理指出,在严格的假设下,经常应用的似然比检验具有最高的统计检验能力,因此可能满足要求。然而,应用程序变得更加困难,因为大多数决策问题是非线性的,因此,参数的概率密度函数不属于众所周知的统计检验分布集。此外,如果应用似然比检验的线性近似,则统计检验功率可能会改变。研究了非线性对假设检验的影响,并用平面坐标变换举例说明了非线性对假设检验的影响。虽然可以想象几个数学等价表达式来评估转换的旋转参数,但相关假设检验的决策以及因此产生的第1类和第2类决策错误的概率彼此不等。基于蒙特卡罗积分,估计有效决策误差,并将其作为评估线性和非线性等价的基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations
Abstract In geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pearson lemma states that under strict assumptions the often-applied likelihood ratio test has highest statistical test power and may thus fulfill the requirement. The application, however, is made more difficult as most of the decision problems are non-linear and, thus, the probability density function of the parameters does not belong to the well-known set of statistical test distributions. Moreover, the statistical test power may change, if linear approximations of the likelihood ratio test are applied. The influence of the non-linearity on hypothesis testing is investigated and exemplified by the planar coordinate transformations. Whereas several mathematical equivalent expressions are conceivable to evaluate the rotation parameter of the transformation, the decisions and, thus, the probabilities of type 1 and 2 decision errors of the related hypothesis testing are unequal to each other. Based on Monte Carlo integration, the effective decision errors are estimated and used as a basis of valuation for linear and non-linear equivalents.
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来源期刊
Journal of Geodetic Science
Journal of Geodetic Science REMOTE SENSING-
CiteScore
1.90
自引率
7.70%
发文量
3
审稿时长
14 weeks
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