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Sources of variability in AUC
Published in Dev P. Chakraborty, Observer Performance Methods for Diagnostic Imaging, 2017
There are other options available for estimating case sampling variance of AUC, and this chapter is not intended to be comprehensive. Three commonly used options are described: the DeLong et al. method, the bootstrap, and the jackknife resampling methods.
Fast and Exact Leave-One-Out Analysis of Large-Margin Classifiers
Published in Technometrics, 2022
We repeat the above for . The leave-one-out analysis is closely tied to jackknife resampling that was proposed for bias and variance estimation of an estimator. Although bootstrap has replaced jackknife in statistical inference (Efron 1982), the leave-one-out analysis is still widely used in assessing the predictive accuracy of a model, that is, the cross-validation method. As early as 1969, it was shown that the leave-one-out cross-validation yields a nearly unbiased estimator of the predictor error (Luntz and Brailovsky 1969). In 1979, Golub, Heath, and Wahba (1979) studied the leave-one-out analysis of ridge regression. Their result directly motivated us to conduct the research in this article, so it is necessary to review their work. The ridge regression is , where . The solution is , where is the ith column of H, and X is the matrix whose ith row is . Consider the same ridge regression with the ith observation removed: then the mean-squared leave-one-out cross-validation error is , which is denoted by . Golub, Heath, and Wahba (1979) showed the following Golub-Heath-Wahba formula:where hii is the ith diagonal element of matrix H. It is important to see that Equation (3) is directly from the following leave-one-out residual formula: which can be extended to a family of linear smoothers including smoothing splines and kernel ridge regression (Wahba and Wold 1975; Wahba 1977; Craven and Wahba 1978; Hastie, Tibshirani, and Friedman 2009). In other words, the Golub-Heath-Wahba formula holds for a wide class of nonparametric regression methods as well. Equation (3) was recently used to improve the Mallow’s Cp (Rosset and Tibshirani 2020). The leave-one-out analysis was also used as a predictive inference tool in Barber et al. (2021).