A class of logistic-type discriminant functions Export

@article{citeulike:2736265, abstract = {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. 10.1093/biomet/89.1.1}, author = {Eguchi, Shinto and Copas, John}, citeulike-article-id = {2736265}, citeulike-linkout-0 = {http://dx.doi.org/10.1093/biomet/89.1.1}, citeulike-linkout-1 = {http://biomet.oxfordjournals.org/cgi/content/abstract/89/1/1}, doi = {10.1093/biomet/89.1.1}, journal = {Biometrika}, keywords = {auc, class\_probability\_estimation, classification, logistic, loss, neyman-pearson, roc, weighting}, month = {March}, number = {1}, pages = {1--22}, posted-at = {2008-04-30 06:53:14}, priority = {0}, title = {A class of logistic-type discriminant functions}, url = {http://dx.doi.org/10.1093/biomet/89.1.1}, volume = {89}, year = {2002} }

TY - JOUR ID - citeulike:2736265 L3 - citeulike-article-id:2736265 N2 - 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. 10.1093/biomet/89.1.1 IS - 1 JF - Biometrika EP - 22 TI - A class of logistic-type discriminant functions VL - 89 SP - 1 KW - auc KW - class_probability_estimation KW - classification KW - logistic KW - loss KW - neyman-pearson KW - roc KW - weighting AU - Eguchi, Shinto AU - Copas, John PY - 2002/03/01/ UR - http://dx.doi.org/10.1093/biomet/89.1.1 ER -