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This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general…

Methodology · Statistics 2026-01-13 Hao-Xuan Sun , Song Xi Chen , Yumou Qiu

Probabilistic forecasting of high dimensional multivariate time series is a notoriously challenging task, both in terms of computational burden and distribution modeling. Most previous work either makes simple distribution assumptions or…

Machine Learning · Computer Science 2021-01-27 Nam Nguyen , Brian Quanz

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

Computation · Statistics 2019-01-18 Shaoxin Wang , Hu Yang , Chaoli Yao

A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or…

Methodology · Statistics 2016-08-30 Esa Ollila , Ilya Soloveychik , David E. Tyler , Ami Wiesel

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

Ecess-over-Threshold method is a crucial technique in extreme value analysis, which approximately models larger observations over a threshold using a Generalized Pareto Distribution. This paper presents a comprehensive framework for…

Methodology · Statistics 2025-06-03 Yifan Hu , Yanxi Hou

For factor model, the involved covariance matrix often has no row sparse structure because the common factors may lead some variables to strongly associate with many others. Under the ultra-high dimensional paradigm, this feature causes…

Methodology · Statistics 2014-09-22 Junlong Zhao , Hongyu Zhao , Lixing Zhu

Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…

Statistics Theory · Mathematics 2023-06-21 Elad Romanov , Gil Kur , Boaz Nadler

This survey provides a self-contained account of $M$-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying $M$-functionals and discuss their weak continuity and differentiability. This is…

Statistics Theory · Mathematics 2015-03-20 Lutz Duembgen , Markus Pauly , Thomas Schweizer

We propose an end-to-end trainable approach for multi-instance pose estimation, called POET (POse Estimation Transformer). Combining a convolutional neural network with a transformer encoder-decoder architecture, we formulate multiinstance…

Computer Vision and Pattern Recognition · Computer Science 2021-12-22 Lucas Stoffl , Maxime Vidal , Alexander Mathis

In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha>0 of a distribution is proposed. It is based on the fact that block-maxima of size m of the independent and identically distributed data scale at a…

Statistics Theory · Mathematics 2007-06-13 Stilian A. Stoev , George Michailidis , Murad S. Taqqu

In this article, we introduce a two-way factor model for a high-dimensional data matrix and study the properties of the maximum likelihood estimation (MLE). The proposed model assumes separable effects of row and column attributes and…

Methodology · Statistics 2021-03-17 Gao Zhigen , Yuan Chaofeng , Jing Bingyi , Huang Wei , Guo Jianhua

Recent years have seen rapid advances in the data-driven analysis of dynamical systems based on Koopman operator theory and related approaches. On the other hand, low-rank tensor product approximations -- in particular the tensor train (TT)…

Numerical Analysis · Mathematics 2021-08-11 Feliks Nüske , Patrick Gelß , Stefan Klus , Cecilia Clementi

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Yingying Fan , Jinchi Lv

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Machine Learning · Statistics 2016-06-03 Jinghui Chen , Quanquan Gu

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

Methodology · Statistics 2012-10-01 Jushan Bai , Yuan Liao

Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…

Methodology · Statistics 2024-08-21 Wei Liu , Qingzhi Zhong

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…

Computation · Statistics 2019-07-10 Cheng Wang , Binyan Jiang

Tyler's M-estimator is a well known procedure for robust and heavy-tailed covariance estimation. Tyler himself suggested an iterative fixed-point algorithm for computing his estimator however, it requires super-linear (in the size of the…

Optimization and Control · Mathematics 2022-10-27 Lior Danon , Dan Garber

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