Hypothesis Testing for High-Dimensional Matrix-Valued Data

2024-12-10 · Shijie Cui, Danning Li, Runze Li, Lingzhou Xue

This paper addresses hypothesis testing for the mean of matrix-valued data in high-dimensional settings. We investigate the minimum discrepancy test, originally proposed by Cragg (1997), which serves as a rank test for lower-dimensional matrices. We evaluate the performance of this test as the matrix dimensions increase proportionally with the sample size, and identify its limitations when matrix dimensions significantly exceed the sample size. To address these challenges, we propose a new test statistic tailored for high-dimensional matrix rank testing. The oracle version of this statistic is analyzed to highlight its theoretical properties. Additionally, we develop a novel approach for constructing a sparse singular value decomposition (SVD) estimator for singular vectors, providing a comprehensive examination of its theoretical aspects. Using the sparse SVD estimator, we explore the properties of the sample version of our proposed statistic. The paper concludes with simulation studies and two case studies involving surveillance video data, demonstrating the practical utility of our proposed methods.

📄 PDF Abstract BibTeX arXiv:2412.07987

Code (0)

등록된 구현이 없습니다.

Testing the martingale difference hypothesis in high dimension

2022-09-11 · Jinyuan Chang, Qing Jiang, Xiaofeng Shao

In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear depen…

Time Series Time Series Analysis valid Vocal Bursts Intensity Prediction

Tensor Graphical Model: Non-convex Optimization and Statistical Inference

2016-09-15 · Xiang Lyu, Will Wei Sun, Zhaoran Wang, Han Liu 외

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each w…

Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality

2014-08-09 · Vikas Sindhwani, Ha Quang Minh, Aurelie Lozano

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that …

Causal Inference Generalization Bounds regression

Nearly Optimal Sample Size in Hypothesis Testing for High-Dimensional Regression

2013-11-01 · Adel Javanmard, Andrea Montanari

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach use…

regression Two-sample testing Vocal Bursts Intensity Prediction

Goodness-of-Fit Tests for Inhomogeneous Random Graphs

2020-01-01 · ICML 2020 1 · Soham Dan, Bhaswar B. Bhattacharya

Hypothesis testing of random networks is an emerging area of modern research, especially in the high-dimensional regime, where the number of samples is smaller or comparable to the size of the graph. In this paper we c…

Two-sample testing