Cross-Validation for Correlated Data

Generalized Cross-Validation for Correlated Data (GCVc)

Since its introduction by Stone (1974) and Geisser (1975), cross-validation has been studied and improved by several authors including Burman et al. the most widely used and best known is generalized cross-validation (GCV) (Craven & Wahba, 1979), which establishes a single-pass method that penalizes the fit by the trace of the smoother matrix assuming independent errors. We propose an extension...

Generalized Correlated Cross-Validation (GCCV)

Multiple Wavelet Threshold Estimation by Generalized Cross Validation for Data with Correlated Noise

De-noising algorithms based on wavelet thresholding replace small wavelet coeecients by zero and keep or shrink the coeecients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use Generalized Cross Validation. This procedure does not require an estimation for the noise ...

Generalised Cross Validation for Noise-Free Data

Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...