Related papers: Hypothesis testing for eigenspaces of covariance m…
In many areas of machine learning, it becomes necessary to find the eigenvector decompositions of large matrices. We discuss two methods for reducing the computational burden of spectral decompositions: the more venerable Nystom extension…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…
We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…
The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…
This paper studies the impact of bootstrap procedure on the eigenvalue distributions of the sample covariance matrix under a high-dimensional factor structure. We provide asymptotic distributions for the top eigenvalues of bootstrapped…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique…
In addition to the commonly analyzed measures of location, dispersion measurements such as variance and correlation provide many valuable information. Consequently, they play a crucial role in multivariate statistics, which leads to tests…
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…
Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In…