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Traditional covariate selection methods for causal inference focus on achieving unbiasedness and asymptotic efficiency. In many practical scenarios, researchers must estimate causal effects from observational data with limited sample sizes…
We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain $\mathcal D\subset \mathbb R^d$, with Besov-tree random coefficients. This is to say that the logarithms of the diffusion…
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods…
This paper proposes factor stochastic volatility models with skew error distributions. The generalized hyperbolic skew t-distribution is employed for common-factor processes and idiosyncratic shocks. Using a Bayesian sparsity modeling…
The purpose of this article is to develop the dimension reduction techniques in panel data analysis when the number of individuals and indicators is large. We use Principal Component Analysis (PCA) method to represent large number of…
Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under…
A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
In the analysis of cluster data, the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model…
We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…
This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…
Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates…
Multiparticle collision dynamics (MPC), a particle-based mesoscale simulation technique for com- plex fluid, is widely employed in non-equilibrium simulations of soft matter systems. To maintain a defined thermodynamic state, thermalization…