Related papers: Minimum Hellinger distance estimates for a periodi…

A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…

Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

In the recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi-parametric asymptotic theory, comparable to the one developed…

We consider a new method of the semiparametric statistical estimation for the continuous-time moving average L\'evy processes. We derive the convergence rates of the proposed estimators, and show that these rates are optimal in the minimax…

The simple interpretation of the minimum distance of a linear code obtained by De Boer and Pellikaan, and later refined by the second author, is further developed through the study of various finitely generated graded modules. We use the…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…

We study the problem of learning clusters of partially observed linear dynamical systems from multiple input-output trajectories. This setting is particularly relevant when there are limited observations (e.g., short trajectories) from…

In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of…

In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a stochastic boundary value problem from a prior probability…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

We introduce methods and theory for fractionally cointegrated curve time series. We develop a variance-ratio test to determine the dimensions associated with the nonstationary and stationary subspaces. For each subspace, we apply a local…

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…

We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…

We consider Stochastic Volatility processes with heavy tails and possible long memory in volatility. We study the limiting conditional distribution of future events given that some present or past event was extreme (i.e. above a level which…

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into…

Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…