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

Empirical likelihood is a powerful semi-parametric method increasingly investigated in the literature. However, most authors essentially focus on an i.i.d. setting. In the case of dependent data, the classical empirical likelihood method…

We present a new approach to the bootstrap for chains of infinite order taking values on a finite alphabet. It is based on a sequential Bootstrap Central Limit Theorem for the sequence of canonical Markov approximations of the chain of…

The main objective of this paper is to establish bootstrap uniform functional central limit theorem for Harris recurrent Markov chains over uniformly bounded classes of functions. We show that the result can be generalized also to the…

We consider Gaussian and bootstrap approximations for the supremum of additive functionals of aperiodic Harris recurrent Markov chains. The supremum is taken over a function class that may depend on the sample size, which allows for…

We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…

We consider the residual-based or naive bootstrap for functional autoregressions of order 1 and prove that it is asymptotically valid for, e.g., the sample mean and for empirical covariance operator estimates. As a crucial auxiliary result,…

We propose and analyze a model-based bootstrap for transition kernels in finite controlled Markov chains (CMCs) with possibly nonstationary or history-dependent control policies, a setting that arises naturally in offline reinforcement…

While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed…

The block maxima method is a standard approach for analyzing the extremal behavior of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved…

This paper proposes a valid bootstrap-based distributional approximation for M-estimators exhibiting a Chernoff (1964)-type limiting distribution. For estimators of this kind, the standard nonparametric bootstrap is inconsistent. The method…

Using the regenerative scheme of Comets, Fern\'andez and Ferrari (2002), we establish a functional central limit theorem (FCLT) for discrete time stochastic processes (chains) with summable memory decay. Furthermore, under stronger…

We provide a functional central limit theorem for a broad class of smooth functions for possibly noncausal multivariate linear processes with time-varying coefficients. Since the limiting processes depend on unknown quantities, we propose a…

We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show…

Bootstrap techniques (also called resampling computation techniques) have introduced new advances in modeling and model evaluation. Using resampling methods to construct a series of new samples which are based on the original data set,…

Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…

Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…

This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…

A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric,…

Functional times series have become an integral part of both functional data and time series analysis. This paper deals with the functional autoregressive model of order 1 and the autoregression bootstrap for smooth functions. The…