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Estimates for the generalized cross-validation function via an extrapolation and statistical approach

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Abstract

Generalized cross-validation (GCV) is a popular tool for specifying the tuning parameter in linear regression model or equivalently the regularization parameter in Tikhonov regularization. In this work, we are concerned with the estimation and minimization of the GCV function by using a combination of an extrapolation procedure and a statistical approach. In particular, we derive families of estimates for the GCV function. By minimizing the estimated GCV function over a grid of values, a GCV estimate of the regularization parameter is achieved. We present several numerical examples to illustrate the effectiveness of the derived families of estimates for approximating the regularization parameter for several linear discrete ill-posed problems.

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Acknowledgements

The authors are grateful to the reviewers of this paper whose valuable remarks improved significantly this work. The work of the second author (P. R.) was implemented with a scholarship from State Scholarships Foundation (IKY) which was funded by the Act “Scholarship Program for postgraduate studies of a second cycle of studies” from resources of the OP “Human Resources Development, Education and Lifelong Learning”, 2014-2020 with the co-financing of the European Social Fund (ESF) and the Greek State.

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  1. Department of Mathematics, University of Athens, Panepistimiopolis, 15784, Athens, Greece

    Marilena Mitrouli & Paraskevi Roupa

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  1. Marilena Mitrouli
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  2. Paraskevi Roupa
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Correspondence to Marilena Mitrouli.

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Mitrouli, M., Roupa, P. Estimates for the generalized cross-validation function via an extrapolation and statistical approach. Calcolo 55, 24 (2018). https://doi.org/10.1007/s10092-018-0266-3

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  • DOI: https://doi.org/10.1007/s10092-018-0266-3

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