相关论文: On Finite Time Span Estimators of Parameters for O…

We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Auto-regressive sequence generative models trained by Maximum Likelihood Estimation suffer the exposure bias problem in practical finite sample scenarios. The crux is that the number of training samples for Maximum Likelihood Estimation is…

Research in NLP is often supported by experimental results, and improved reporting of such results can lead to better understanding and more reproducible science. In this paper we analyze three statistical estimators for expected validation…

A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$ is described by a Markov process in two dimensions. But even though there exists a…

Maximum likelihood estimates are often biased. It is shown that this pathology is inherent to the traditional ML estimation method for two or more parameters, thus motivating from a different angle the use of MCMLE.

Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…

We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with…

Regularized system identification has become a significant complement to more classical system identification. It has been numerically shown that kernel-based regularized estimators often perform better than the maximum likelihood estimator…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

\noindent \textbf{Abstract}: We consider the parameter estimation problem for the Ornstein-Uhlenbeck process $X$ driven by a fractional Ornstein-Uhlenbeck process $V$, i.e. the pair of processes defined by the non-Markovian continuous-time…

We propose a new unbiased estimator for estimating the utility of the optimal stopping problem. The MUSE, short for Multilevel Unbiased Stopping Estimator, constructs the unbiased Multilevel Monte Carlo (MLMC) estimator at every stage of…

This paper deals with the rate of convergence for the central limit theorem of estimators of the drift coefficient, denoted $\theta$, for a Ornstein-Uhlenbeck process $X \coloneqq \{X_t,t\geq0\}$ observed at high frequency. We provide an…

The aim of this work is to estimate the drift coefficient of a fractional heat equation driven by an additive space-time noise using the Maximum likelihood estimator (MLE). In the first part of the paper, the first $N$ Fourier modes of the…

We derive the optimal energy error estimate for multiscale finite element method with oversampling technique applying to elliptic system with rapidly oscillating periodic coefficients under the assumption that the coefficients are bounded…

We study an optimal execution problem in the presence of market impact where the security price follows a geometric Ornstein-Uhlenbeck process, which implies the mean-reverting property, and show that the optimal strategy is a mixture of…

Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…

A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…

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…

We examine a mean-reverting Ornstein-Uhlenbeck process that perturbs an unknown Lipschitz-continuous drift and aim to estimate the drift's value at a predetermined time horizon by sampling the path of the process. Due to the time varying…