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We derive confidence intervals (CIs) and confidence sequences (CSs) for the classical problem of estimating a bounded mean. Our approach generalizes and improves on the celebrated Chernoff method, yielding the best closed-form "empirical-Bernstein" CSs and ...
This thesis focuses on two kinds of statistical inference problems in signal processing and data science. The first problem is the estimation of a structured informative tensor from the observation of a noisy tensor in which it is buried. The structure com ...
Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...
In this paper we propose an unbiased Monte Carlo maximum likelihood estimator for discretely observed Wright-Fisher diffusions. Our approach is based on exact simulation techniques that are of special interest for diffusion processes defined on a bounded d ...
We present an extended validation of semi-analytical, semi-empirical covariance matrices for the two-point correlation function (2PCF) on simulated catalogs representative of luminous red galaxies (LRGs) data collected during the initial 2 months of operat ...
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...
We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically ...
Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports injuries in ath ...
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the eigenfunctions of the hom ...
