Related papers: Information Geometry and Asymptotics for Kronecker…

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…

This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…

A severe limitation of many nonparametric estimators for random coefficient models is the exponential increase of the number of parameters in the number of random coefficients included into the model. This property, known as the curse of…

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…

Nonsingular estimation of high dimensional covariance matrices is an important step in many statistical procedures like classification, clustering, variable selection an future extraction. After a review of the essential background…

We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality, we impose an additional assumption on the structure of the covariance matrix $\Sigma$. To be more…

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…

We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…

Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…

This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite…

This paper deals with improvement of linear quantile regression, when there are a few distinct values of the covariates but many replicates. On can improve asymptotic efficiency of the estimated regression coefficients by using suitable…

High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…

We incorporate into the empirical measure the auxiliary information given by a finite collection of expectation in an optimal information geometry way. This allows to unify several methods exploiting a side information and to uniquely…

When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…

We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…

Partial coherence is an important quantity derived from spectral or precision matrices and is used in seismology, meteorology, oceanography, neuroscience and elsewhere. If the number of complex degrees of freedom only slightly exceeds the…

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

The improvement of resummation algorithms for divergent perturbative expansions in quantum field theory by asymptotic information about perturbative coefficients is investigated. Various asymptotically optimized resummation prescriptions…