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Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…

We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…

For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local…

Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…

Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data…

In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…

We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and…

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

The empirical Bayes estimators in mixed models are useful for small area estimation in the sense of increasing precision of prediction for small area means, and one wants to know the prediction errors of the empirical Bayes estimators based…

Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs (ARX) when both the system orders and parameters are unknown. We design distributed…

In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…

The paper focuses on the Vasicek model driven by a tempered fractional Brownian motion. We derive the asymptotic distributions of the least-squares estimators (based on continuous-time observations) for the unknown drift parameters. This…

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…

Causal decomposition analysis provides a way to identify mediators that contribute to health disparities between marginalized and non-marginalized groups. In particular, the degree to which a disparity would be reduced or remain after…

This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…