Optimality of training/test size and resampling effectiveness in cross-validation

Methodological Considerations in the Statistical Modeling of Catastrophe Bond Prices

“…Absolute errors, differentially weighted according to the sign of the error, lead to specific quantiles and the method of quantile regression. Afendras and Markatou () emphasize the role of the loss function in determining the optimal choice of cross‐validation parameters, and, in particular, explore Efron's () “q‐class” of loss functions.…”

Distance Metrics and Clustering Methods for Mixed‐type Data

“…Other related resampling‐based methods for identifying the number of clusters include Dudoit & Fridlyand (), Lange et al (), Levine & Domany () and Volkovich et al (). Using the prediction strength method requires a choice of test/training set size in the cross‐validation step, a challenging problem that has received some general attention in the literature (Afendras & Markatou, ; Markatou et al , ) but has not been investigated in the context of prediction strength. Additionally, the choice of threshold in the prediction strength method is recommended to be 0.8–0.9 for well‐separated clusters (Tibshirani & Walther, ), but in the event of clusters with less separation, or heterogeneous levels of separation, it is unclear how to best select a threshold.…”

Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

“…To deduce Lemma 3.5, observe that on the set (1). By applying [23, Lemma 3], for any δ > 0 we can find a tight sequence (N n ) in R for which L n k n |ξ n − ξ 0 | γ ≤ δ|ξ n − ξ 0 | ρ + N n k ρ/(ρ−γ) n .…”

“…We refer to [7], [10], [14], [24], [26], and [27] for some related results. Also, [1] recently discussed optimal selection of random and k-fold cross-validation estimators, the theoretical backbone of which involves some moment bounds of the estimators used; the related paper [2] studied the uniform integrability of the ordinary least-squares estimator in the linear regression setting. In the standard asymptotics, the polynomial type large deviation inequality (PLDI) of [33], which estimates the tail of L(û n ) in such a way that sup r>0 sup n>0 r L P (|û n | ≥ r) < ∞ for a given L > 0, provides us with a widely-applicable tool for verifying the convergence of moments.…”