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Optimization algorithms that leverage gradient covariance information, such as variants of natural gradient descent (Amari, 1998), offer the prospect of yielding more effective descent directions. For models with many parameters, the…

In multivariate time series analysis, spectral coherence measures the linear dependency between two time series at different frequencies. However, real data applications often exhibit nonlinear dependency in the frequency domain.…

Let $Y$ be a Gaussian vector of $\mathbb{R}^n$ of mean $s$ and diagonal covariance matrix $\Gamma$. Our aim is to estimate both $s$ and the entries $\sigma_i=\Gamma_{i,i}$, for $i=1,...,n$, on the basis of the observation of two independent…

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…

A crucial task for a randomized controlled trial (RCT) is to specify a statistical method that can yield an efficient estimator and powerful test for the treatment effect. A novel and effective strategy to obtain efficient and powerful…

We consider applying stochastic approximation (SA) methods to solve nonsmooth variational inclusion problems. Existing studies have shown that the averaged iterates of SA methods exhibit asymptotic normality, with an optimal limiting…

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…

We investigate the optimality for model selection of the so-called slope heuristics, $V$-fold cross-validation and $V$-fold penalization in a heteroscedastic with random design regression context. We consider a new class of linear models…

Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…

When outcome data are expensive or onerous to collect, scientists increasingly substitute predictions from machine learning and AI models for unlabeled cases, a process which has consequences for downstream statistical inference. While…

We discuss the statistical analysis method for the worldvolume hybrid Monte Carlo (WV-HMC) algorithm [arXiv:2012.08468], which was recently introduced to substantially reduce the computational cost of the tempered Lefschetz thimble method.…

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…

We consider statistical inference for errors-in-variables regression models with dependent observations under the high dimensionality of the error covariance matrix. It is tempting to prewhiten the model and data that had led to efficient…

Mixed-frequency Vector AutoRegressions (MF-VAR) model the dynamics between variables recorded at different frequencies. However, as the number of series and high-frequency observations per low-frequency period grow, MF-VARs suffer from the…

Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…

During the last two decades, locally stationary processes have been widely studied in the time series literature. In this paper we consider the locally-stationary vector-auto-regression model of order one, or LS-VAR(1), and estimate its…

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access to their local data streams. We focus on the case where agents seek…

We present a novel black box optimization algorithm called Hessian Estimation Evolution Strategy. The algorithm updates the covariance matrix of its sampling distribution by directly estimating the curvature of the objective function. This…