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Related papers: Drift Estimation for Discretely Sampled SPDEs

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This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares…

Probability · Mathematics 2022-03-11 Pavel Kříž , Jana Šnupárková

We study approximate maximum likelihood estimators (MLEs) for the parameters of the widely used Heston stock and volatility stochastic differential equations (SDEs). We compute explicit closed form estimators maximizing the discretized…

Probability · Mathematics 2015-06-19 Robert Azencott , Yutheeka Gadhyan

In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise. We propose a new class of…

Statistics Theory · Mathematics 2016-11-15 Igor Cialenco , Ruoting Gong , Yicong Huang

We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…

Probability · Mathematics 2019-08-22 Antoine Lejay , Paolo Pigato

We study asymptotic behavior of maximum likelihood estimator for a time inhomogeneous diffusion process given by a SDE $dX_t=\alpha b(t)X_t dt + \sigma(t) dB_t$, $t\in[0,T)$, with a parameter $\alpha\in R$, where $T\in(0,\infty]$ and…

Statistics Theory · Mathematics 2010-05-25 Matyas Barczy , Gyula Pap

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and H\"older continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods…

Methodology · Statistics 2026-05-19 Bowen Fang , Dario Spanò , Massimiliano Tamborrino

Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…

Statistics Theory · Mathematics 2013-03-21 Uwe Küchler , Michael Sørensen

Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically…

Statistics Theory · Mathematics 2018-06-29 Hiroyuki Kasahara , Katsumi Shimotsu

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…

Statistics Theory · Mathematics 2023-05-30 Kai Tan , Pierre C. Bellec

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases:…

Statistics Theory · Mathematics 2018-06-08 Matyas Barczy , Mohamed Ben Alaya , Ahmed Kebaier , Gyula Pap

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…

Probability · Mathematics 2009-06-18 Pavel Chigansky

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance 54 (1999)…

Statistics Theory · Mathematics 2012-03-12 Jinyuan Chang , Song Xi Chen

The problem of estimating a parameter in the drift coefficient is addressed for $N$ discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints,…

Statistics Theory · Mathematics 2024-10-17 Chiara Amorino , Arnaud Gloter , Hélène Halconruy

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

Statistics Theory · Mathematics 2010-01-13 Piet Groeneboom , Geurt Jongbloed , Birgit I. Witte

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 address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…

Methodology · Statistics 2025-07-31 Konstantin E. Avrachenkov , Leonid B. Freidovich

We consider drift parameter estimation in a model driven by the sum of two independent fractional Brownian motions with different Hurst indices. Although the maximum likelihood estimator (MLE) for this model is known theoretically, its…

Probability · Mathematics 2026-03-06 Yuliya Mishura , Kostiantyn Ralchenko , Mykyta Yakovliev

Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…

Machine Learning · Computer Science 2024-06-05 Jen Ning Lim , Juan Kuntz , Samuel Power , Adam M. Johansen

This paper deals with the problem of inference associated with linear fractional diffusion process with random effects in the drift. In particular we are concerned with the maximum likelihood estimators (MLE) of the random effect…

Statistics Theory · Mathematics 2019-12-04 El Omari Mohamed , Hamid El Maroufy , Christiane Fuchs

In this paper we are interested in the Maximum Likelihood Estimator (MLE) of the vector parameter of an autoregressive process of order $p$ with regular stationary Gaussian noise. We exhibit the large sample asymptotical properties of the…

Statistics Theory · Mathematics 2013-04-23 Alexandre Brouste , Chunhao Cai , Marina Kleptsyna