Fast cross-validation of high-breakdown resampling methods for PCA
Computational Statistics & Data Analysis
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Combining regular and irregular histograms by penalized likelihood
Computational Statistics & Data Analysis
Estimation of the proportion of true null hypotheses in high-dimensional data under dependence
Computational Statistics & Data Analysis
Segmentation of the mean of heteroscedastic data via cross-validation
Statistics and Computing
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The problem of density estimation is addressed by minimization of the L^2-risk for both histogram and kernel estimators. This quadratic risk is estimated by leave-p-out cross-validation (LPO), which is made possible thanks to closed formulas, contrary to common belief. The potential gain in the use of LPO with respect to V-fold cross-validation (V-fold) in terms of the bias-variance trade-off is highlighted. An exact quantification of this extra variability, induced by the preliminary random partition of the data in the V-fold, is proposed. Furthermore, exact expressions are derived for both the bias and the variance of the risk estimator with histograms. Plug-in estimates of these quantities are provided, while their accuracy is assessed thanks to concentration inequalities. An adaptive selection procedure for p in the case of histograms is subsequently presented. This relies on minimization of the mean square error of the LPO risk estimator. Finally a simulation study is carried out which first illustrates the higher reliability of the LPO with respect to the V-fold, and then assesses the behavior of the selection procedure. For instance optimality of leave-one-out (LOO) is shown, at least empirically, in the context of regular histograms.