Related papers: Covariance Operator Estimation: Sparsity, Lengthsc…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
This paper develops efficient ensemble Kalman filter (EnKF) implementations based on shrinkage covariance estimation. The forecast ensemble members at each step are used to estimate the background error covariance matrix via the…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
The estimation of causal treatment effects from observational data is a fundamental problem in causal inference. To avoid bias, the effect estimator must control for all confounders. Hence practitioners often collect data for as many…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…
Koopman operator theory provides a global linear representation of nonlinear dynamics and underpins many data-driven methods. In practice, however, finite-dimensional feature spaces induced by a user-chosen dictionary are rarely invariant,…
In many situations, when dealing with several populations, equality of the covariance operators is assumed. An important issue is to study if this assumption holds before making other inferences. In this paper, we develop a test for…
Let $X,X_1,\dots, X_n,\dots$ be i.i.d. centered Gaussian random variables in a separable Banach space $E$ with covariance operator $\Sigma:$ $$ \Sigma:E^{\ast}\mapsto E,\ \ \Sigma u = {\mathbb E}\langle X,u\rangle, u\in E^{\ast}. $$ The…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…
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…
High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the \emph{unobservable} parameter vector. However, neither…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a…
Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline…
It is now well understood that $\ell_1$ minimization algorithm is able to recover sparse signals from incomplete measurements [2], [1], [3] and sharp recoverable sparsity thresholds have also been obtained for the $\ell_1$ minimization…
In this work, we study the emergence of sparsity and multiway structures in second-order statistical characterizations of dynamical processes governed by partial differential equations (PDEs). We consider several state-of-the-art multiway…