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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…

Statistics Theory · Mathematics 2025-11-14 Carsten H. Chong , Fabian Mies

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

Statistics Theory · Mathematics 2025-05-19 Yuzhong Cheng , Hiroki Masuda

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has…

Information Theory · Computer Science 2008-04-17 Alexander Schoenhuth

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

Statistics Theory · Mathematics 2023-07-10 Alexandre Lecestre

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

Statistics Theory · Mathematics 2025-01-17 Cristina Butucea , Alexander Meister , Angelika Rohde

The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…

Probability · Mathematics 2015-10-28 Chii-Ruey Hwang , Raoul Normand , Sheng-Jhih Wu

We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…

Statistics Theory · Mathematics 2019-10-17 János Marcell Benke , Gyula Pap

We develop a theory of local asymptotic normality in the quantum domain based on a noncommutative extension of the Lebesgue decomposition. This formulation gives a substantial generalization of the previous paper [Yamagata, Fujiwara, and…

Quantum Physics · Physics 2017-03-23 Akio Fujiwara , Koichi Yamagata

Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is…

Statistics Theory · Mathematics 2019-08-02 Simon Holbach

We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…

Statistics Theory · Mathematics 2018-09-03 Cathrine Aeckerle-Willems , Claudia Strauch

The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…

Statistics Theory · Mathematics 2015-03-19 Han Xiao , Wei Biao Wu

We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposedd that under the basic hypothesis the trend coefficient depends on the finite…

Statistics Theory · Mathematics 2013-05-16 M. Kleptsyna , Yu. A. Kutoyants

In this paper, we consider a diffusion process with jumps whose drift and jump coefficient depend on an unknown parameter. We then give a self-contained proof of the local asymptotic mixed normality (LAMN) property when the process is…

Probability · Mathematics 2016-11-26 Ngoc Khue Tran , Eulalia Nualart

It is well-known that density estimation on the unit interval is asymptotically equivalent to a Gaussian white noise experiment, provided the densities have H\"older smoothness larger than $1/2$ and are uniformly bounded away from zero. We…

Statistics Theory · Mathematics 2018-10-29 Kolyan Ray , Johannes Schmidt-Hieber

Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in…

Probability · Mathematics 2016-02-24 Anne Marie Svane

We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…

Probability · Mathematics 2026-02-12 Leonid Koralov , Chenglin Liu

In this paper we find nonasymptotic exponential upper bounds for the deviation in the ergodic theorem for families of homogeneous Markov processes. We find some sufficient conditions for geometric ergodicity uniformly over a parametric…

Probability · Mathematics 2012-05-10 Leonid Galtchouk , Serguei Pergamenchtchikov

This paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null…

Statistics Theory · Mathematics 2012-10-23 Alexei Onatski , Marcelo J. Moreira , Marc Hallin

A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…

Analysis of PDEs · Mathematics 2022-08-12 Taras A. Mel'nyk , Arsen V. Klevtsovskiy

We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only…

Analysis of PDEs · Mathematics 2020-11-17 Antonio De Rosa , Domenico Angelo La Manna