Related papers: Projection inference for high-dimensional covarian…

We show that the limiting variance of a sequence of estimators for a structured covariance matrix has a general form that appears as the variance of a scaled projection of a random matrix that is of radial type and a similar result is…

Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

We consider shrinkage estimation of higher order Hilbert space valued Bochner integrals in a non-parametric setting. We propose estimators that shrink the $U$-statistic estimator of the Bochner integral towards a pre-specified target…

This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…

Stochastic gradient methods are central to large-scale learning, but they treat mini-batch gradients as unbiased estimators, which classical decision theory shows are inadmissible in high dimensions. We formulate gradient computation as a…

We consider detection and localization of an abrupt break in the covariance structure of high-dimensional random data. The paper proposes a novel testing procedure for this problem. Due to its nature, the approach requires a properly chosen…

When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…

In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…

Risk assessment of hurricane-driven storm surge relies on deterministic computer models that produce outputs over a large spatial domain. The surge models can often be run at a range of fidelity levels, with greater precision yielding more…

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…

Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…

We investigate predictive densities for multivariate normal models with unknown mean vectors and known covariance matrices. Bayesian predictive densities based on shrinkage priors often have complex representations, although they are…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background…

We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…

We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is…