The e-MoM approach for approximating matrix functionals

Fika, Paraskevi; Mitrouli, Marilena; Roupa, Paraskevi; Triantafyllou, Dimitrios

doi:10.1016/j.cam.2019.04.023

Cited by 3 publications

(1 citation statement)

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“…Although the assumption that the index of proximity is close to one may seem restrictive, it turns out to be satisfied very often. For example, it was shown heuristically that the index of proximity is around one for matrices arising from discrete ill-posed problems with error contaminated data [2]. Analytical proofs were given for linear regression models in case when the covariates have the same variance and correlation [7,8].…”

Section: Estimation Of the Generalised Cross Validation Function Via Extrapolationmentioning

confidence: 99%

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

Koukouvinos

Jbilou

Mitrouli

et al. 2019

ELA

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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.

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Section: Estimation Of the Generalised Cross Validation Function Via Extrapolationmentioning

confidence: 99%