# Oracle inequalities for sign constrained generalized linear models

@article{Koike2019OracleIF,
title={Oracle inequalities for sign constrained generalized linear models},
author={Yuta Koike and Yuta Tanoue},
journal={Econometrics and Statistics},
year={2019}
}
• Published 9 November 2017
• Computer Science
• Econometrics and Statistics
2 Citations

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## References

SHOWING 1-10 OF 31 REFERENCES

### Sign-constrained least squares estimation for high-dimensional regression

Network tomography is shown to be an application where the necessary conditions for success of non-negative least squares are naturally fulfilled and empirical results confirm the effectiveness of the sign constraint for sparse recovery.

### Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization

• Computer Science
• 2012
It is argued further that in specific cases, NNLS may have a better $\ell_{\infty}$-rate in estimation and hence also advantages with respect to support recovery when combined with thresholding, and from a practical point of view, NnLS does not depend on a regularization parameter and is hence easier to use.

### Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

• Mathematics, Computer Science
• 2001
In this article, penalized likelihood approaches are proposed to handle variable selection problems, and it is shown that the newly proposed estimators perform as well as the oracle procedure in variable selection; namely, they work as well if the correct submodel were known.

### Oracle Inequalities for Convex Loss Functions with Nonlinear Targets

• Mathematics
• 2013
This article considers penalized empirical loss minimization of convex loss functions with unknown target functions. Using the elastic net penalty, of which the Least Absolute Shrinkage and Selection

### Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming

• Computer Science
• 2011
A pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant, which achieves near-oracle performance, attaining the convergence rate σl(s/n) log pr-super-1/2 in the prediction norm.

### On the conditions used to prove oracle results for the Lasso

• Mathematics
• 2009
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the

### Quasi-Likelihood and/or Robust Estimation in High Dimensions

• Mathematics, Computer Science
• 2012
An extension of the oracle results to the case of quasi-likelihood loss is presented, and bounds for the prediction error and $\ell_1$-error are proved and it is shown that under an irrepresentable condition, the $\ell-1$-penalized quasi- likelihood estimator has no false positives.

### On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations

• Mathematics
IEEE Transactions on Information Theory
• 2008
It is shown that for matrices A with a row-span intersecting the positive orthant, if this problem admits a sufficiently sparse solution, it is necessarily unique, and the bound on the required sparsity depends on a coherence property of the matrix A.

### AIC for the Lasso in generalized linear models

• Computer Science
• 2016
A criterion is derived from the original deﬁnition of the AIC, that is, an asymptotically unbiased estimator of the Kullback-Leibler divergence that becomes the Gaussian regression setting of the Lasso and can be regarded as its generalization.

### The Adaptive Lasso and Its Oracle Properties

A new version of the lasso is proposed, called the adaptive lasso, where adaptive weights are used for penalizing different coefficients in the ℓ1 penalty, and the nonnegative garotte is shown to be consistent for variable selection.