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SpaceX
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NASA
СпутникиРНSpaceXРоскосмосNASASimultaneous estimation and variable selection become difficult in linear models when the design is high-dimensional and predictors are correlated. Although the Lasso and related shrinkage estimators control model complexity, their selection can be inconsistent under certain conditions. To address this, we propose the triple shrinkage adaptive GO estimator, which extends the GO framework with adaptive, coefficient-specific weights. This multi-level shrinkage produces flexible penalization and achieves oracle properties asymptotically, yielding performance comparable to methods that effectively know the true support. The new estimator preserves the grouping effect, a key characteristic of the adaptive ElasticNet, such that coefficients of highly correlated predictors are shrunk toward one another. An efficient algorithm compatible with existing Lasso solutions makes this estimator computationally viable. The proposed approach, therefore, offers a robust alternative for improving estimation accuracy and support recovery in sparse linear models with dependent predictors.
Simultaneous estimation and variable selection become difficult in linear models when the design is high-dimensional and predictors are correlated. Although the Lasso and related shrinkage estimators control model complexity, their selection can be inconsistent under certain conditions. To address this, we propose the triple shrinkage adaptive GO estimator, which extends the GO framework with adaptive, coefficient-specific weights. This multi-level shrinkage produces flexible penalization and achieves oracle properties asymptotically, yielding performance comparable to methods that effectively know the true support. The new estimator preserves the grouping effect, a key characteristic of the adaptive ElasticNet, such that coefficients of highly correlated predictors are shrunk toward one another. An efficient algorithm compatible with existing Lasso solutions makes this estimator computationally viable. The proposed approach, therefore, offers a robust alternative for improving estimation accuracy and support recovery in sparse linear models with dependent predictors.
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The datasets analyzed in this study are publicly available through the Comprehensive R Archive Network (CRAN). Specifically, the diabetes dataset is available in the elasticnet package and the NIR spectroscopy biscuit dough dataset is available in the ppls package.
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Decision Sciences Area, Indian Institute of Management Lucknow, Lucknow, Uttar Pradesh, India
Ramakrushna Mishra, Akshay Mishra & Gaurav Garg
Authors
Correspondence to Akshay Mishra.
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Mishra, R., Mishra, A. & Garg, G. An adaptive triple-shrinkage framework for linear models with oracle properties. Comput Stat 41, 108 (2026). https://doi.org/10.1007/s00180-026-01788-6
Received: 24 May 2025
Accepted: 10 July 2026
Published: 21 July 2026
Version of record: 21 July 2026
DOI: https://doi.org/10.1007/s00180-026-01788-6