Related papers: Regenerative bootstrap for $\beta$-null recurrent …

The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient…

We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

We consider strictly stationary stochastic processes of Hilbert space-valued random variables and focus on fully functional tests for the equality of the lag-zero autocovariance operators of several independent functional time series. A…

The problem of quantifying uncertainty about the locations of multiple change points by means of confidence intervals is addressed. The asymptotic distribution of the change point estimators obtained as the local maximisers of moving sum…

Traditional inference in cointegrating regressions requires tuning parameter choices to estimate a long-run variance parameter. Even in case these choices are "optimal", the tests are severely size distorted. We propose a novel…

For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…

Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

We discuss the peculiar features of the renormalization procedure in the case of infinite-component effective theory. It is shown that in the case of physically interesting theories (namely, those leading to the amplitudes with asymptotic…

This guide aims at providing a general introduction to bootstrap methods. By using simple examples taken from nuclear physics, I discuss how such a method can be used to quantify error bars of an estimator. I also investigate the use of…

Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often…

This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…

We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…

We consider long-range dependent data. It is shown that the bootstrapped empirical process of these data converges to a semi-degenerate limit. The random part of this limit is always Gaussian. Thus the bootstrap might fail when the original…

Motivated by applications in telecommunications, computer scienceand physics, we consider a discrete-time Markov process withrestart. At each step the process eitherwith a positive probability restarts from a given distribution, orwith the…

A model-free bootstrap procedure for a general class of stationary time series is introduced. The theoretical framework is established, showing asymptotic validity of bootstrap confidence intervals for many statistics of interest. In…

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based…

In this paper, we comprehensively study the inductive biases of two major approaches to augmenting Transformers with a recurrent mechanism: (1) the approach of incorporating a depth-wise recurrence similar to Universal Transformers; and (2)…

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an…