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Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…

Statistics Theory · Mathematics 2025-07-09 Mitsuki Kobayashi , Yuto Nishiwaki , Yasutaka Shimizu , Nobutoki Takaoka

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…

Statistics Theory · Mathematics 2024-01-31 Patricia Román-Román , Juan José Serrano-Pérez , Francisco Torres-Ruiz

The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…

Methodology · Statistics 2018-11-13 Susanne Ditlevsen , Adeline Samson

This paper deals with the estimation problem of misspecified ergodic L\'evy driven stochastic differential equation models based on high-frequency samples. We utilize the widely applicable and tractable Gaussian quasi-likelihood approach…

Statistics Theory · Mathematics 2018-07-11 Yuma Uehara

In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…

Statistics Theory · Mathematics 2019-09-24 Evgeny Pchelintsev , Svyatoslav Perelevskiy , Irina Makarova

This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…

Statistics Theory · Mathematics 2009-09-03 Yoichi Nishiyama

In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$, two unknown parameters. We suppose that the process is discretely observed at the…

Statistics Theory · Mathematics 2020-11-30 Chiara Amorino , Arnaud Gloter

We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…

Statistical Mechanics · Physics 2019-05-01 N. Leibovich , E. Barkai

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…

Statistics Theory · Mathematics 2022-01-20 Tetsuya Kawai , Masayuki Uchida

In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and…

Statistics Theory · Mathematics 2013-09-27 Emeline Schmisser

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…

Statistics Theory · Mathematics 2014-06-17 Matyas Barczy , Leif Doering , Zenghu Li , Gyula Pap

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

Statistics Theory · Mathematics 2010-08-18 Jimmy Olsson , Jonas Ströjby

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

Machine Learning · Statistics 2026-01-23 Lei Qian , Wu Su , Yanqi Huang , Song Xi Chen

We consider covariance parameter estimation for a Gaussian process under inequality constraints (boundedness, monotonicity or convexity) in fixed-domain asymptotics. We address the estimation of the variance parameter and the estimation of…

Statistics Theory · Mathematics 2021-11-04 François Bachoc , Agnès Lagnoux , Andrés F. López-Lopera

We study Bayes procedures for the problem of nonparametric drift estimation for one-dimensional, ergodic diffusion models from discrete-time, low-frequency data. We give conditions for posterior consistency and verify these conditions for…

Statistics Theory · Mathematics 2013-02-01 Frank van der Meulen , Harry van Zanten

We consider statistical inference for a class of mixed-effects models with system noise described by a non-Gaussian integrated Ornstein-Uhlenbeck process. Under the asymptotics where the number of individuals goes to infinity with possibly…

Statistics Theory · Mathematics 2025-11-18 Takumi Imamura , Hiroki Masuda

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

Methodology · Statistics 2021-03-10 Sai Li , Tony T. Cai , Hongzhe Li

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…

Machine Learning · Computer Science 2022-06-22 Siavash Ameli , Shawn C. Shadden

We study sufficient conditions for local asymptotic mixed normality. We weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhya Ser. A 1982) so that they can be applied to a wider class of statistical models including a…

Statistics Theory · Mathematics 2021-05-04 Teppei Ogihara , Yuma Uehara

Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…

Statistics Theory · Mathematics 2025-01-29 Dmytro Marushkevych , Francisco Pina , Mark Podolskij