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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…
In this article, we study the critical growth rates of dimension below which Gaussian critical values can be used for hypothesis testing but beyond which they cannot. We are particularly interested in how these growth rates depend on the…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…
Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian beta matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic…
Let $\mathbf{X} = (X_i)_{1\leq i \leq n}$ be an i.i.d. sample of square-integrable variables in $\mathbb{R}^d$, \GB{with common expectation $\mu$ and covariance matrix $\Sigma$, both unknown.} We consider the problem of testing if $\mu$ is…
Given a linear dynamical system, we consider the problem of constructing an approximate system using only a subset of the sensors out of the total set such that the observability Gramian of the new system is approximately equal to that of…
In this paper, we establish a high-dimensional CLT for the sample mean of $p$-dimensional spatial data observed over irregularly spaced sampling sites in $\mathbb{R}^d$, allowing the dimension $p$ to be much larger than the sample size $n$.…
Recently, it was shown that the probability distribution function (PDF) of the free energy of a single continuum directed polymer (DP) in a random potential, equivalently of the height of a growing interface described by the…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time.…
Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no…
We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…
We solve the largest sample eigenvalue distribution problem in the rank 1 spiked model of the quaternionic Wishart ensemble, which is the first case of a statistical generalization of the Laguerre symplectic ensemble (LSE) on the soft edge.…
We establish the relation between two objects: an integrable system related to Painlev\'e II equation, and the symplectic invariants of a certain plane curve S(TW). This curve describes the average eigenvalue density of a random hermitian…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
The top eigenvalues of rank $r$ spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for…