Related papers: Bootstrapping spectral statistics in high dimensio…
A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
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…
In clinical trials the comparison of two different populations is a frequently addressed problem. Non-linear (parametric) regression models are commonly used to describe the relationship between covariates as the dose and a response…
In this paper, our objective is to present a constraining principle governing the spectral properties of the sample covariance matrix. This principle exhibits harmonious behavior across diverse limiting frameworks, eliminating the need for…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
In this paper, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to…
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…
Multivariate time series present many challenges, especially when they are high dimensional. The paper's focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices…
Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when…
In this paper we propose a new test of heteroscedasticity for parametric regression models and partial linear regression models in high dimensional settings. When the dimension of covariates is large, existing tests of heteroscedasticity…
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…
The problem of comparing the entire second order structure of two functional processes is considered and a $L^2$-type statistic for testing equality of the corresponding spectral density operators is investigated. The test statistic…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population…