Related papers: $\ell_1$-Regularized Generalized Least Squares
In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…
This paper develops the asymptotic theory of a Fully Modified Generalized Least Squares estimator for multivariate cointegrating polynomial regressions. Such regressions allow for deterministic trends, stochastic trends and integer powers…
Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…
This study proposes sparse estimation methods for the generalized linear models, which run one of least angle regression (LARS) and least absolute shrinkage and selection operator (LASSO) in the tangent space of the manifold of the…
We present a new iterative rotation inversion technique based on the Simultaneous Algebraic Reconstruction Technique developed for image reconstruction. We describe in detail our algorithmic implementation and compare it to the classical…
Tuning a complex simulation code refers to the process of improving the agreement of a code calculation with respect to a set of experimental data by adjusting parameters implemented in the code. This process belongs to the class of inverse…
Recently, the proposal of the least mean square (LMS) and recursive least squares (RLS) algorithm for graph signal processing (GSP) provides excellent solutions for processing signals defined on irregular structures such as sensor networks.…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under…
Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized…
Two new methods are proposed for linear regression analysis for data with measurement errors. Both methods are designed to accommodate intrinsic scatter in addition to measurement errors. The first (BCES) is a direct extension of the…
Noise problems in signals have gained huge attention due to the need of noise-free output signal in numerous communication systems. The principal of adaptive noise cancellation is to acquire an estimation of the unwanted interfering signal…