Related papers: Parametric estimation for functional autoregressiv…
Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are…
We propose novel parameter estimation algorithms for a class of dynamical systems with nonlinear parametrization. The class is initially restricted to smooth monotonic functions with respect to a linear functional of the parameters. We show…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Parametric modeling of non-stationary signals is addressed in this article. We present several models based on the characteristic features of the modeled signal, together with the methods for accurate estimation of model parameters.…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
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…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
The paper presents new asymptotic recurrent algorithms of phase space reduction for regularly and singularly perturbed semi-Markov processes. These algorithms give effective conditions of weak convergence for distributions and convergence…
We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
We propose a chirp-like signal model as an alternative to a chirp model and a generalisation of the sinusoidal model, which is a fundamental model in the statistical signal processing literature. It is observed that the proposed model can…
In this paper, we consider a partially linear model of the form $Y_t=X_t^{\tau}\theta_0+g(V_t)+\epsilon_t$, $t=1,...,n$, where $\{V_t\}$ is a $\beta$ null recurrent Markov chain, $\{X_t\}$ is a sequence of either strictly stationary or…
We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
Least squares estimator of the stability parameter $\varrho := |\alpha| + |\beta|$ for a spatial unilateral autoregressive process $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\varepsilon_{k,\ell}$ is investigated. Asymptotic…
This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov…
The goal of this paper is to extend the nonparametric estimation of Impulse Response Functions (IRF) by means of local projections in the nonlinear dynamic framework. We discuss the existence of a nonlinear autoregressive representation for…
Two adaptive bandwidth selection methods for nonparametric estimators in locally stationary processes are proposed. We investigate a cross validation approach and a method based on contrast minimization and derive asymptotic properties of…