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非参数回归中部分交叉验证、GCV 与随机化 GCV 的渐近比较AI 解读

When using nonparametric estimates of the mean curve, surface or image underlying noisy observations, the selection of "smoothing parameters" is generally crucial. This paper gives a theoretical comparison of the performances of generalized cross-validation (GCV) and of its fast randomized version (RGCV), as selection criteria. This is mainly done by studying the asymptotic distribution of the excess error for each selector, that is, the difference between the (data-driven)…

Ridge regression is a well-known technique to estimate the coefficients of a linear model. The method of regularization is a similar approach commonly used to solve underdetermined linear equations with discrete noisy data. When applying such a technique, the choice of the smoothing (or regularization) parameter $h$ is crucial. Generalized cross-validation (GCV) and Mallows' $C_L$ are two popular methods for estimating a good value for $h,$ from the data. Their asymptotic…