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High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…

Methodology · Statistics 2020-09-18 Xiang Lyu , Jian Kang , Lexin Li

In this paper we prove multilevel concentration inequalities for bounded functionals $f = f(X_1, \ldots, X_n)$ of random variables $X_1, \ldots, X_n$ that are either independent or satisfy certain logarithmic Sobolev inequalities. The…

Probability · Mathematics 2020-06-16 Friedrich Götze , Holger Sambale , Arthur Sinulis

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…

Methodology · Statistics 2016-05-17 T. Tony Cai , Anru Zhang

Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…

Statistics Theory · Mathematics 2022-07-04 Huiming Zhang , Haoyu Wei

We consider asymptotically exact inference on the leading canonical correlation directions and strengths between two high dimensional vectors under sparsity restrictions. In this regard, our main contribution is the development of a loss…

Statistics Theory · Mathematics 2022-02-10 Nilanjana Laha , Nathan Huey , Brent Coull , Rajarshi Mukherjee

We propose a method to impose homogeneous linear inequality constraints of the form $Ax\leq 0$ on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the…

Machine Learning · Computer Science 2020-05-29 Thomas Frerix , Matthias Nießner , Daniel Cremers

We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model P rather than on the typically unknown true model Q. Our proposed method combines…

Information Theory · Computer Science 2017-07-04 Konstantinos Gourgoulias , Markos A. Katsoulakis , Luc Rey-Bellet , Jie Wang

We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish lower bounds on the rates of convergence of the estimators of the…

Statistics Theory · Mathematics 2012-02-07 Debashis Paul , Iain M. Johnstone

This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed…

Probability · Mathematics 2026-05-19 Jiaheng Chen , Daniel Sanz-Alonso

Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…

Statistics Theory · Mathematics 2019-03-05 Li Jialiang , Lv Jing

Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…

Machine Learning · Computer Science 2024-10-10 Agus Hartoyo , Jan Argasiński , Aleksandra Trenk , Kinga Przybylska , Anna Błasiak , Alessandro Crimi

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…

Methodology · Statistics 2026-05-15 Wenhao Zhang , Zhaoxing Gao

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

Methodology · Statistics 2025-11-04 Shihao Wu , Gongjun Xu , Ji Zhu

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Optimization and Control · Mathematics 2022-11-23 Quentin Jacquet , Riadh Zorgati

Self-normalized processes arise naturally in many learning-related tasks. While self-normalized concentration has been extensively studied for scalar-valued processes, there are few results for multidimensional processes outside of the…

Probability · Mathematics 2025-05-02 Justin Whitehouse , Zhiwei Steven Wu , Aaditya Ramdas

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

Statistics Theory · Mathematics 2026-03-10 Raunak Shevade , Monika Bhattacharjee

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

Statistics Theory · Mathematics 2011-03-21 Jérôme Dedecker , Florence Merlevède , Magda Peligrad

This work considers stationary vector count time series models defined via deterministic functions of a latent stationary vector Gaussian series. The construction is very general and ensures a pre-specified marginal distribution for the…

Statistics Theory · Mathematics 2023-10-31 Marie-Christine Düker , Robert Lund , Vladas Pipiras

This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…