Related papers: Asymptotic Anytime-Valid Inference for U-statistic…

We establish normal approximation in the Wasserstein metric for both non-degenerate and degenerate second-order U-statistics under cross-sectional dependence using Stein's method. For the non-degenerate case, our results extend recent…

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…

Motivated by the problem of online canonical correlation analysis, we propose the \emph{Stochastic Scaled-Gradient Descent} (SSGD) algorithm for minimizing the expectation of a stochastic function over a generic Riemannian manifold. SSGD…

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a…

Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…

For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…

This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…

We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise. Recent applications in machine learning motivate the need to understand finite-time error rates, but conventional stochastic approximation…

In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…

In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result,…

It is shown how the central limit theorem for U-statistics of spatial Poisson point processes can help to derive the central limit theorem for U-statistics of a Gibbs facet process from stochastic geometry. A full-dimensional submodel…

In this paper, we investigate time-varying nonlinear time series regression for a broad class of locally stationary time series. First, we propose sieve nonparametric estimators for the time-varying regression functions that achieve uniform…

We develop Gaussian approximations for high-dimensional vectors formed by second-order $U$- and $V$-statistics whose kernels depend on sample size under independent but not identically distributed (i.n.i.d.) sampling. Our results hold…

Due to the increasing complexity of technical systems, accurate first principle models can often not be obtained. Supervised machine learning can mitigate this issue by inferring models from measurement data. Gaussian process regression is…

We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with successive minimum Euclidean distance encoding under the quadratic distortion measure. Specifically, we…

When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…

The problem of network-constrained averaging is to compute the average of a set of values distributed throughout a graph G using an algorithm that can pass messages only along graph edges. We study this problem in the noisy setting, in…