Related papers: Continuous Record Asymptotics for Change-Points Mo…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter…
We consider the problem of locating a jump discontinuity (change-point) in a smooth parametric regression model with a bounded covariate. It is assumed that one can sample the covariate at different values and measure the corresponding…
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the…
In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the…
High-dimensional changepoint inference that adapts to various change patterns has received much attention recently. We propose a simple, fast yet effective approach for adaptive changepoint testing. The key observation is that two…
We address the problem of searching for a change point in an anomalous process among a finite set of M processes. Specifically, we address a composite hypothesis model in which each process generates measurements following a common…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
Most of the literature on change-point analysis by means of hypothesis testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 : \theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the process before and…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
Change point detection in high dimensional data has found considerable interest in recent years. Most of the literature either designs methodology for a retrospective analysis, where the whole sample is already available when the…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…