Related papers: On Parameter Estimation for Cusp-type Signals
The human brain copes with sensory uncertainty in accordance with Bayes' rule. However, it is unknown how the brain makes predictions in the presence of parameter uncertainty. Here, we tested whether and how humans take parameter…
Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…
Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…
Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…
We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex…
This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…
We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible…
This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
A model of Poissonian observation having a jump (change-point) in the intensity function is considered. Two cases are studied. The first one corresponds to the situation when the jump size converges to a non-zero limit, while in the second…
The pure tone hearing threshold is usually estimated from responses to stimuli at a set of standard frequencies. This paper describes a probabilistic approach to the estimation problem in which the hearing threshold is modelled as a smooth…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
This paper presents a novel Bayesian strategy for the estimation of smooth signals corrupted by Gaussian noise. The method assumes a smooth evolution of a succession of continuous signals that can have a numerical or an analytical…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs…
The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation…