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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…

Econometrics · Economics 2021-04-21 Karsten Schweikert

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Statistics Theory · Mathematics 2014-02-14 Anders Bredahl Kock

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…

Methodology · Statistics 2017-10-31 Felix Abramovich , Daniela De Canditiis , Marianna Pensky

This paper considers the problem of estimating a periodic function in a continuous time regression model with a general square integrable semimartingale noise. A model selection adaptive procedure is proposed. Sharp non-asymptotic oracle…

Statistics Theory · Mathematics 2009-09-18 Victor Konev , Serguei Pergamenchtchikov

In this paper, we study the statistical behaviour of the Exponentially Weighted Aggregate (EWA) in the problem of high-dimensional regression with fixed design. Under the assumption that the underlying regression vector is sparse, it is…

Statistics Theory · Mathematics 2016-11-28 Arnak S. Dalalyan , Edwin Grappin , Quentin Paris

Selection of important covariates and to drop the unimportant ones from a high-dimensional regression model is a long standing problem and hence have received lots of attention in the last two decades. After selecting the correct model, it…

Statistics Theory · Mathematics 2019-09-17 Debraj Das , Arindam Chatterjee , S. N. Lahiri

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…

Methodology · Statistics 2018-12-07 Sokbae Lee , Yuan Liao , Myung Hwan Seo , Youngki Shin

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general…

Machine Learning · Statistics 2018-06-27 Pierre Alquier , Benjamin Guedj

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

Statistics Theory · Mathematics 2018-11-26 Takumi Suzuki , Nakahiro Yoshida

We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation…

Statistics Theory · Mathematics 2024-05-20 Julien Aubert , Luc Lehéricy , Patricia Reynaud-Bouret

We consider the nonparametric regression and the classification problems for $\psi$-weakly dependent processes. This weak dependence structure is more general than conditions such as, mixing, association, $\ldots$. A penalized estimation…

Machine Learning · Statistics 2023-03-03 William Kengne , Modou Wade

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…

Statistics Theory · Mathematics 2017-08-03 Jianqing Fan , Runlong Tang , Xiaofeng Shi

We introduce a general approach to prove oracle properties in context tree selection. The results derive from a concentration condition that is verified, for example, by mixing processes. Moreover, we show the superiority of the oracle…

Statistics Theory · Mathematics 2011-11-10 A. Garivier , M. Lerasle

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…

Statistics Theory · Mathematics 2012-09-18 Ery Arias-Castro , Karim Lounici

This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for…

Methodology · Statistics 2022-02-08 Shaomin Li , Haoyu Wei , Xiaoyu Lei

We consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares…

Statistics Theory · Mathematics 2013-11-13 Dong Dai , Philippe Rigollet , Lucy Xia , Tong Zhang

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty.…

Machine Learning · Statistics 2015-07-07 Huan Gui , Quanquan Gu

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…

Statistics Theory · Mathematics 2015-04-08 Niels Richard Hansen , Patricia Reynaud-Bouret , Vincent Rivoirard

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…

Statistics Theory · Mathematics 2013-02-04 Shujie Ma , Qiongxia Song , Li Wang

In this paper, we introduce structured sparsity estimators in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018) recently for fixed design and normal errors.…

Machine Learning · Statistics 2021-04-30 Mehmet Caner