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Whereas diverse variations of diffusion models exist, extending the linear diffusion into a nonlinear diffusion process is investigated by very few works. The nonlinearity effect has been hardly understood, but intuitively, there would be…

Machine Learning · Computer Science 2022-10-14 Dongjun Kim , Byeonghu Na , Se Jung Kwon , Dongsoo Lee , Wanmo Kang , Il-Chul Moon

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter $\lambda$ and the Hurst index of such processes…

Statistics Theory · Mathematics 2012-07-11 Saeid Rezakhah , Anne Philippe , Navideh Modarresi

In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…

Computation · Statistics 2026-05-01 Jingning Yao , Ajay Jasra , Sheng Jiang

Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…

Methodology · Statistics 2025-03-17 Jan Albrecht , Sebastian Reich

Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…

Statistics Theory · Mathematics 2026-02-20 Hugo Chardon , Matthieu Lerasle , Jaouad Mourtada

We study structural equation modeling (SEM) for diffusion processes with jumps. Based on high-frequency data, we consider the parameter estimation and the goodness-of-fit test in the SEM. Using a threshold method, we propose the…

Statistics Theory · Mathematics 2025-05-20 Shogo Kusano , Masayuki Uchida

The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…

Probability · Mathematics 2026-05-01 Fabian Mies , Duuk Sikkens

In this paper, we consider stochastic versions of three classical growth models given by ordinary differential equations (ODEs). Indeed we use stochastic versions of Von Bertalanffy, Gompertz, and Logistic differential equations as models.…

Applications · Statistics 2023-12-22 F. Baltazar-Larios , F. J. Delgado-Vences , A. Ornelas Vargas

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Statistics Theory · Mathematics 2017-12-05 Shogo H. Nakakita , Masayuki Uchida

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of…

Probability · Mathematics 2015-05-19 Kestutis Kubilius , Viktor Skorniakov , Dmitrij Melichov

In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…

Probability · Mathematics 2023-05-25 Yuliya Mishura , Anton Yurchenko-Tytarenko

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

This paper presents a new parameter estimation method for It\^{o} diffusions such that the resulting model predicts the equilibrium statistics as well as the sensitivities of the underlying system to external disturbances. Our formulation…

Numerical Analysis · Mathematics 2017-05-24 John Harlim , Xiantao Li , He Zhang

This research aims to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the…

In some non-regular statistical estimation problems, the limiting likelihood processes are functionals of fractional Brownian motion (fBm) with Hurst's parameter H; 0 < H <=? 1. In this paper we present several analytical and numerical…

Statistics Theory · Mathematics 2014-06-06 Alexander Novikov , Nino Kordzakhia , Timothy Ling

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…

Statistics Theory · Mathematics 2021-03-01 Meng Yuan , Pengfei Li , Changbao Wu

I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…

Machine Learning · Statistics 2019-10-30 George Papamakarios

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…

Machine Learning · Computer Science 2025-12-03 Shuhan Zheng , Ziqiang Li , Kantaro Fujiwara , Gouhei Tanaka

The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new…

Methodology · Statistics 2007-09-04 Emma J. McCoy , Sofia C. Olhede , David A. Stephens