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Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…

Methodology · Statistics 2024-10-17 Yuan Gao , Zhiyuan Zhang , Zhanrui Cai , Xuening Zhu , Tao Zou , Hansheng Wang

Recent research has focused on $\ell_1$ penalized least squares (Lasso) estimators for high-dimensional linear regressions in which the number of covariates $p$ is considerably larger than the sample size $n$. However, few studies have…

Statistics Theory · Mathematics 2022-05-05 Yuefeng Han , Ruey S. Tsay

Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to…

Methodology · Statistics 2014-12-24 Qing Zhou

Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…

Methodology · Statistics 2014-03-19 Kasper Brink-Jensen , Claus Thorn Ekstrøm

A Stochastic Simulator (SS) is proposed, based on a semiclassical description of the radiation-matter interaction, to obtain an efficient description of the lasing transition for devices ranging from the nanolaser to the traditional…

Optics · Physics 2015-02-09 G. P. Puccioni , G. L. Lippi

We consider estimation of a functional parameter of a realistically modeled data distribution based on observing independent and identically distributed observations. We define an $m$-th order Spline Highly Adaptive Lasso Minimum Loss…

Statistics Theory · Mathematics 2021-07-05 Mark J. van der Laan , David Benkeser , Weixin Cai

The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of non-smooth penalty functions for the sample covariance matrix, and demonstrate how this method…

Methodology · Statistics 2018-05-23 David E. Tyler , Mengxi Yi

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…

Methodology · Statistics 2025-06-26 Sourav Chatterjee , Trevor Hastie , Robert Tibshirani

We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…

Statistics Theory · Mathematics 2023-06-28 Fan Wang , Oscar Hernan Madrid Padilla , Yi Yu , Alessandro Rinaldo

Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…

Methodology · Statistics 2011-01-04 Xia Cui , Heng Peng , Songqiao Wen , Lixing Zhu

The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…

Statistics Theory · Mathematics 2017-01-23 Yannick Baraud , Lucien Birgé , Mathieu Sart

Surface-based data is commonly observed in diverse practical applications spanning various fields. In this paper, we introduce a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based…

Methodology · Statistics 2024-03-12 Zhiling Gu , Shan Yu , Guannan Wang , Ming-Jun Lai , Li Wang

With a focus on linear models with smooth functional covariates, we propose a penalization framework (SACR) based on the nonzero centered ridge, where the center of the penalty is optimally reweighted in a supervised way, starting from the…

Methodology · Statistics 2020-11-03 Edoardo Belli

In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic…

Statistics Theory · Mathematics 2014-05-27 Richard Lockhart , Jonathan Taylor , Ryan J. Tibshirani , Robert Tibshirani

We present a new methodology for simultaneous variable selection and parameter estimation in function-on-scalar regression with an ultra-high dimensional predictor vector. We extend the LASSO to functional data in both the $\textit{dense}$…

Statistics Theory · Mathematics 2016-10-25 Rina Foygel Barber , Matthew Reimherr , Thomas Schill

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account…

Machine Learning · Computer Science 2011-09-14 Edouard Grave , Guillaume Obozinski , Francis Bach

The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…

Methodology · Statistics 2020-01-01 Heng Peng , Chuanlong Xie , Jingxin Zhao

In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its…

Machine Learning · Statistics 2020-09-04 Mathurin Massias , Quentin Bertrand , Alexandre Gramfort , Joseph Salmon

There has been much recent work on inference after model selection when the noise level is known, however, $\sigma$ is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the…

Statistics Theory · Mathematics 2017-02-13 Xiaoying Tian , Joshua R. Loftus , Jonathan E. Taylor

For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…

Methodology · Statistics 2022-09-29 Xin Xin , Boyi Xie , Yunhai Xiao