A class of logistic-type discriminant functions
A class of logistic-type discriminant functions
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DOI：
10.1093/biomet/89.1.1
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发表时间：
2002-03-01
期刊：
影响因子：
2.7
通讯作者：
Copas, J
中科院分区：
文献类型：
--
作者：
Eguchi, S;Copas, J
在两组判别分析中，Neyman-Pearson引理表明，任意线性函数的ROC曲线，即接收者工作特征曲线，到处低于真实似然比的ROC曲线。这两条曲线之间的加权面积可以用作寻找好的判别函数的风险函数。权重函数对应于分析的目标，例如最小化错误分类的预期成本，或最大化ROC下的面积。所得到的判别函数可以通过迭代重加权逻辑回归来估计。我们研究了“近逻辑”设置中的一些渐近性质，其中我们假设协变量已经选择，使得线性函数给出了合理的，但不一定是精确的，真实对数似然比的近似值。本文讨论了一些例子，包括对乳腺细胞学医学诊断的研究。
In two-group discriminant analysis, the Neyman-Pearson Lemma establishes that the ROC, receiver operating characteristic, curve for an arbitrary linear function is everywhere below the ROC curve for the true likelihood ratio. The weighted area between these two curves can be used as a risk function for finding good discriminant functions. The weight function corresponds to the objective of the analysis, for example to minimise the expected cost of misclassification, or to maximise the area under the ROC. The resulting discriminant functions can be estimated by iteratively reweighted logistic regression. We investigate some asymptotic properties in the 'near-logistic' setting, where we assume the covariates have been chosen such that a linear function gives a reasonable, but not necessarily exact, approximation to the true log likelihood ratio. Some examples are discussed, including a study of medical diagnosis in breast cytology.