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We propose some parametric tests for ergodic diffusion-plus-noise model, which is a version of state-space modelling in statistics for stochastic diffusion equations. The test statistics are classified into three types:…

Statistics Theory · Mathematics 2018-04-06 Shogo H. Nakakita , Masayuki Uchida

We consider the problem of the construction of the Goodness-of-Fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the…

Statistics Theory · Mathematics 2016-06-17 Maroua Ben Abdeddaiem

This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual…

Statistics Theory · Mathematics 2009-09-02 Estate V. Khmaladze , Hira L. Koul

We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramer-von Mises type is proposed and its asymptotic behavior is studied. We show that under null…

Statistics Theory · Mathematics 2018-06-19 A. S. Dabye , Yu. A. Kutoyants , E. D. Tanguep

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

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

This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…

Methodology · Statistics 2012-02-02 Timothy B. Armstrong

We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…

Statistics Theory · Mathematics 2020-03-30 Reinhard Höpfner , Yury A Kutoyants

We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…

Information Theory · Computer Science 2019-01-30 Qunwei Li , Tiexing Wang , Donald J. Bucci , Yingbin Liang , Biao Chen , Pramod K. Varshney

This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov--Smirnov test based on the…

Statistics Theory · Mathematics 2007-06-13 Hira L. Koul , Shiqing Ling

A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…

Machine Learning · Computer Science 2016-12-15 Shaofeng Zou , Yingbin Liang , H. Vincent Poor , Xinghua Shi

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

Statistics Theory · Mathematics 2011-11-10 Yury A. Kutoyants , Nakahiro Yoshida

This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining…

Statistics Theory · Mathematics 2013-02-20 Hira L. Koul , Ursula U. Müller , Anton Schick

Consider an observation of a multivariate temporal point process $N$ with law $\mathcal P$ on the time interval $[0,T]$. To test the null hypothesis that $\mathcal P$ belongs to a given parametric family, we construct a convergent…

Statistics Theory · Mathematics 2025-06-26 Justin Baars , Sami Umut Can , Roger J. A. Laeven

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…

Statistics Theory · Mathematics 2024-12-16 Yin Tang , Bing Li

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Machine Learning · Statistics 2024-03-08 Gen Li , Yuting Wei , Yuxin Chen , Yuejie Chi

We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…

Statistics Theory · Mathematics 2009-08-25 Rui Song , Michael R. Kosorok , Jason P. Fine

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…

Statistics Theory · Mathematics 2020-02-04 Yinqiu He , Gongjun Xu , Chong Wu , Wei Pan

Let $(X_1,Y_1),\ldots,(X_n,Y_n)$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise…

Statistics Theory · Mathematics 2015-04-03 Sami Umut Can , John H. J. Einmahl , Estate V. Khmaladze , Roger J. A. Laeven

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