Some notes on extremal discriminant analysis
Some notes on extremal discriminant analysis
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DOI：
10.1016/j.jmva.2011.06.012
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
B. G. Manjunath;M. Frick;R. Reiss
中科院分区：
文献类型：
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作者：
B. G. Manjunath;M. Frick;R. Reiss
经典判别分析侧重于高斯和非参数模型，在非参数模型中，未知密度由基于训练样本的核密度代替。在本文中，我们假设它足以基于超过较高阈值的分类，这可以解释为条件框架中的观察结果。因此，只需要对截断分布进行统计建模。在这种情况下，非参数建模是不够的，因为核方法在上尾区域是不准确的。然而，我们可以处理截断的参数分布，比如高斯分布。我们的主要目的是用适当的广义帕累托分布代替截断的高斯分布，并探索两种模型中判别函数的性质和关系。
Classical discriminant analysis focusses on Gaussian and nonparametric models where in the second case the unknown densities are replaced by kernel densities based on the training sample. In the present article we assume that it suffices to base the classification on exceedances above higher thresholds, which can be interpreted as observations in a conditional framework. Therefore, the statistical modeling of truncated distributions is merely required. In this context, a nonparametric modeling is not adequate because the kernel method is inaccurate in the upper tail region. Yet one may deal with truncated parametric distributions like the Gaussian ones. Our primary aim is to replace truncated Gaussian distributions by appropriate generalized Pareto distributions and to explore properties and the relationship of discriminant functions in both models.