Robust trainability of single neurons
Journal of Computer and System Sciences
Computing location depth and regression depth in higher dimensions
Statistics and Computing
Robustness against separation and outliers in logistic regression
Computational Statistics & Data Analysis
On Robustness Properties of Convex Risk Minimization Methods for Pattern Recognition
The Journal of Machine Learning Research
Depth estimators and tests based on the likelihood principle with application to regression
Journal of Multivariate Analysis
Distribution-free tests for polynomial regression based on simplicial depth
Journal of Multivariate Analysis
Response shrinkage estimators in binary regression
Computational Statistics & Data Analysis
Bagging tree classifiers for laser scanning images: a data- and simulation-based strategy
Artificial Intelligence in Medicine
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In this paper, we show that the recent notion of regression depth can be used as a data-analytic tool to measure the amount of separation between successes and failures in the binary response framework. Extending this algorithm, allows us to compute the overlap in data sets which are commonly fitted by logistic or probit regression models. The overlap is the number of observations that would need to be removed to obtain complete or quasi-complete separation, i.e. the situation where the regression parameters are no longer identifiable and the maximum likelihood estimate does not exist. It turns out that the overlap is often quite small. The results are equally useful in linear discriminant analysis.