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The model of partially observed linear stochastic differential equations depending on some unknown parameters is considered. An proximation of the unobserved component is proposed. This approximation is realized in three steps. First an…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise.…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
The problem of parameter estimation by observations of inhomogeneous Poisson processes is considered. The method of moments estimator is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…
We consider the gamma process perturbed by a Brownian motion (independent of the gamma process) as a degradation model. Parameters estimation is studied here. We assume that $n$ independent items are observed at irregular instants. From…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
In this paper, we study equations with nonlinearity in the form of a double-well potential, randomised by a velocity-switching (telegraph) stochastic process. If the speed parameters of the randomisation are small, then this dynamics has…
This paper considers the general signal detection and parameter estimation problem in the presence of colored Gaussian noise disturbance. By modeling the disturbance with an autoregressive process, we present three signal detectors with…
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
Recent studies indicate that the noise characteristics of phasor measurement units (PMUs) can be more accurately described by non-Gaussian distributions. Consequently, estimation techniques based on Gaussian noise assumptions may produce…
In this paper, we analyze the asymptotic properties of the Two-Stage (TS) estimator -- a simulation-based parameter estimation method that constructs estimators offline from synthetic data. While TS offers significant computational…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…
According to standard econometric theory, Maximum Likelihood estimation (MLE) is the efficient estimation choice, however, it is not always a feasible one. In network diffusion models with unobserved signal propagation, MLE requires…
We present a method for blind acoustic parameter estimation from single-channel reverberant speech. The method is structured into three stages. In the first stage, a variational auto-encoder is trained to extract latent representations of…