An Eigenvalue Approach For Estimating The Generalized Cross Validation Function For Correlated Matrices

Abstract

This work proposes a fast estimate for the generalized cross-validation function when the design matrix of an experiment has correlated columns. The eigenvalue structure of this matrix is used to derive probability bounds satisfied by an appropriate index of proximity, which provides a simple and accurate estimate for the numerator of the generalized cross-validation function. The denominator of the function is evaluated by an analytical formula. Several simulation tests performed in statistical models having correlated design matrix with intercept confirm the reliability of the proposed probabilistic bounds and indicate the applicability of the proposed estimate for these models.

Solving High-Dimensional Problems in Statistical Modelling: A Comparative Study

“…. , d. Based on the results presented in [17] for the eigenvalues of the matrix X T X, we record analytic formulae for the singular values of X in the following theorem.…”