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We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An…

Econometrics · Economics 2019-08-28 Patrick Kline , Raffaele Saggio , Mikkel Sølvsten

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

In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…

Statistics Theory · Mathematics 2018-09-13 Hannes Leeb , Nina Senitschnig

In this paper, an outlier elimination algorithm for ellipse/ellipsoid fitting is proposed. This two-stage algorithm employs a proximity-based outlier detection algorithm (using the graph Laplacian), followed by a model-based outlier…

Methodology · Statistics 2009-10-27 Jieqi Yu , Haipeng Zheng , Sanjeev R. Kulkarni , H. Vincent Poor

We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…

Methodology · Statistics 2025-03-06 Zhengke Lu , Long Feng

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

Machine Learning · Computer Science 2019-07-09 Frank Nussbaum , Joachim Giesen

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Data Structures and Algorithms · Computer Science 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients.…

Methodology · Statistics 2026-05-05 Samuel Julian Weisenthal

Our goal is to develop a Bayesian model averaging technique in linear regression models that accommodates heavier tailed error densities than the normal distribution. Motivated by the use of the Huber loss function in the presence of…

Methodology · Statistics 2024-11-26 Shamriddha De , Joyee Ghosh

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

Methodology · Statistics 2023-04-07 Matias Salibian-Barrera

It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…

Statistics Theory · Mathematics 2021-01-26 Piotr Pokarowski , Wojciech Rejchel , Agnieszka Soltys , Michal Frej , Jan Mielniczuk

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…

Numerical Analysis · Computer Science 2010-09-03 Adam C. Zelinski , Vivek K Goyal , Elfar Adalsteinsson

Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…

Information Theory · Computer Science 2016-04-05 Anastasios Kyrillidis , Bubacarr Bah , Rouzbeh Hasheminezhad , Quoc Tran-Dinh , Luca Baldassarre , Volkan Cevher

The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed.…

Applications · Statistics 2020-12-16 Andrea Cappozzo , Francesca Greselin , Thomas Brendan Murphy

We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…

Statistics Theory · Mathematics 2018-06-15 Niharika Gauraha

We address the issue of estimating the regression vector $\beta$ in the generic $s$-sparse linear model $y = X\beta+z$, with $\beta\in\R^{p}$, $y\in\R^{n}$, $z\sim\mathcal N(0,\sg^2 I)$ and $p> n$ when the variance $\sg^{2}$ is unknown. We…

Statistics Theory · Mathematics 2012-11-06 Stéphane Chrétien , Sébastien Darses

Nonlinear estimation in robotics and vision is typically plagued with outliers due to wrong data association, or to incorrect detections from signal processing and machine learning methods. This paper introduces two unifying formulations…

Computer Vision and Pattern Recognition · Computer Science 2021-07-05 Pasquale Antonante , Vasileios Tzoumas , Heng Yang , Luca Carlone

Spatial perception is the backbone of many robotics applications, and spans a broad range of research problems, including localization and mapping, point cloud alignment, and relative pose estimation from camera images. Robust spatial…

Machine Learning · Statistics 2019-07-31 Vasileios Tzoumas , Pasquale Antonante , Luca Carlone

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

Optimization and Control · Mathematics 2017-09-29 Dimitris Bertsimas , Bart Van Parys

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…

Statistics Theory · Mathematics 2016-02-09 Marta García Bárzana , Ana Colubi , Erricos John Kontoghiorghes