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Tuning parameter selection for penalized estimation via R2

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  • Holter, Julia C.
  • Stallrich, Jonathan W.

Abstract

The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation) tend to select models with more predictors than necessary. A simple yet powerful cross validation strategy is proposed which is based on maximizing the squared correlation between the observed and predicted values, rather than minimizing squared error loss for the purposes of support recovery. The strategy can be applied to all penalized least-squares estimators and, under certain conditions, the metric implicitly performs a bias adjustment named the α-modification. When applied to the Lasso estimator, the α-modification is closely related to the relaxed Lasso estimator. The approach is demonstrated on a functional variable selection problem to identify optimal placement of surface electromyogram sensors to control a robotic hand prosthesis.

Suggested Citation

  • Holter, Julia C. & Stallrich, Jonathan W., 2023. "Tuning parameter selection for penalized estimation via R2," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:csdana:v:183:y:2023:i:c:s0167947323000403
    DOI: 10.1016/j.csda.2023.107729
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    References listed on IDEAS

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