We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.
A general design-assisted regression framework in which the estimating criterion depends on both the conditional model for $Y \mid \bfX$ and structured features of the covariate distribution, which improves estimation while preserving first-order prediction performance.
S. Ye, Guan-Bo Wang, Cong Zhang et al.· 0 citations
Estimating the first stage of an instrumental variables (IV) model with the least absolute shrinkage and selection operator (LASSO) requires choosing a dictionary of technical instruments and a penalty level. First-order asymptotic theory offers no guidance on these choices, as any consistent implementation yields a st...
Yu-Kun Ma, Manu Navjeevan, Bogdan Salahub· 0 citations
We provide sufficient conditions for the consistency of penalized least squares procedures that select the order (dimension) of a regression model from a sequence of nested classes, allowing for dependent, martingale-difference errors. The main contribution is to relax the classical identifiability requirement: paramet...
Building on a reparameterization for multivariate linear regression that yields a jointly convex penalized likelihood in the reparameterized regression coefficient matrix and the precision matrix, we show that the resulting scaled Gaussian loss is standard self-concordant. This places the joint estimation problem withi...
This work proposes computationally efficient tests for equality of mean vectors of two or more high-dimensional populations by establishing an equivalence between equality of means and a zero population logistic regression parameter.
The sparse-group pliable Lasso (SGPL) extends the pliable Lasso and group pliable Lasso by combining sparse-group regularization with a predictor-level coupling penalty, enabling simultaneous group-level selection, within-group sparsity, and hierarchical structure between main effects and interactions. We propose a blo...
M. Davoudabadi, Minh T. L. Nguyen, A. Ghatari et al.· 0 citations
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