Related papers: Statistical inference for stationary linear models…
The paper deals with a question of robustness of inferences, carried out on a continuous-time stationary process contaminated by a small trend, to this departure from stationarity. We show that a smoothed periodogram approach to parameter…
Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…
How to construct a suitable measurement matrix is still an open question in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit considerable…
We derive novel explicit formulas for the inverses of truncated block Toeplitz matrices that correspond to a multivariate minimal stationary process. The main ingredients of the formulas are the Fourier coefficients of the phase function…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
The paper establishes error orders for integral limit approximations to the traces of products of Toeplitz matrices generated by integrable real symmetric functions defined on the unit circle. These approximations and the corresponding…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…
Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
In this paper, we consider the estimation and inference of precision matrices of a rich class of locally stationary and nonlinear time series assuming that only one realization of the time series is observed. Using a Cholesky decomposition…
The aim of this work is to give an overview of the recent developments in the area of statistical inference for parabolic stochastic partial differential equations. Significant part of the paper is devoted to the spectral approach, which is…
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…
For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…