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In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

Probability · Mathematics 2013-05-06 Y. -X. Ren , R. Song , R. Zhang

We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the…

Probability · Mathematics 2016-04-21 David Croydon , Stephen Muirhead

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…

Methodology · Statistics 2022-06-20 Haeran Cho , Claudia Kirch

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

Probability · Mathematics 2012-10-12 Bojan Basrak , Danijel Krizmanić , Johan Segers

We provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A…

Statistics Theory · Mathematics 2021-08-20 Nathawut Phandoidaen , Stefan Richter

This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety…

Systems and Control · Electrical Eng. & Systems 2026-05-01 Felix Biertümpfel , Jungbae Chun , Peter Seiler

This paper focuses on vector-valued composite functionals, which may be nonlinear in probability. Our primary goal is to establish central limit theorems for these functionals when mixed estimators are employed. Our study is relevant to the…

Statistics Theory · Mathematics 2025-01-09 Huihui Chen , Darinka Dentcheva , Yang Lin , Gregory J. Stock

We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…

Probability · Mathematics 2025-01-30 Thomas Deschatre , Pierre Gruet , Antoine Lotz

An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…

Methodology · Statistics 2019-04-10 Thomas Pitschel

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

Probability · Mathematics 2015-04-07 Paul Jung , Takashi Owada , Gennady Samorodnitsky

In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms satisfying a second moment condition. This…

Probability · Mathematics 2014-04-02 Yan-Xia Ren , Renming Song , Rui Zhang

New goodness-of-fit tests for Markovian models in time series analysis are developed which are based on the difference between a fully nonparametric estimate of the one-step transition distribution function of the observed process and that…

Statistics Theory · Mathematics 2008-12-18 Michael H. Neumann , Efstathios Paparoditis

We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…

Probability · Mathematics 2022-03-02 Xinpeng Li

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…

Probability · Mathematics 2017-07-27 Andrea Granelli , Almut E. D. Veraart

One of the most widely applied unit root test, Phillips-Perron test, enjoys in general highpowers, but suffers from size distortions when moving average noise exists. As a remedy, thispaper proposes a nonparametric bootstrap unit root test…

Methodology · Statistics 2019-07-23 Nan Zou , Dimitris Politis

In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the…

Probability · Mathematics 2014-10-08 Yan-Xia Ren , Renming Song , Rui Zhang

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…

Probability · Mathematics 2010-05-20 Marta Tyran-Kaminska

We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…

Statistics Theory · Mathematics 2016-09-29 Efstathios Paparoditis , Theofanis Sapatinas

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Machine Learning · Statistics 2020-02-26 Ivan Ustyuzhaninov , Ieva Kazlauskaite , Carl Henrik Ek , Neill D. F. Campbell

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

Probability · Mathematics 2007-05-23 Magda Peligrad , Sergey Utev