English
Related papers

Related papers: Adaptive and non-adaptive estimation for degenerat…

200 papers

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…

Optimization and Control · Mathematics 2019-10-18 Romeo Ortega , Vladislav Gromov , Emmanuel Nuño , Anton Pyrkin , Jose Guadalupe Romero

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…

Methodology · Statistics 2013-02-01 Georgios Fellouris

In the present paper we consider Laplace deconvolution for discrete noisy data observed on the interval whose length may increase with a sample size. Although this problem arises in a variety of applications, to the best of our knowledge,…

Statistics Theory · Mathematics 2013-01-15 Felix Abramovich , Marianna Pensky , Yves Rozenholc

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

Statistics Theory · Mathematics 2020-09-14 Yaozhong Hu , Yuejuan Xi

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

Statistics Theory · Mathematics 2019-11-26 Florian Hildebrandt , Mathias Trabs

The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the…

Statistics Theory · Mathematics 2008-02-07 Dmitrij Celov , Remigijus Leipus , Anne Philippe

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

Optimization and Control · Mathematics 2025-02-03 Koki Okajima , Takashi Takahashi

Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and…

Probability · Mathematics 2008-08-25 D. Loukianova , O. Loukianov

In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and…

Statistics Theory · Mathematics 2023-03-29 Gabriela Ciolek , Dmytro Marushkevych , Mark Podolskij

Many trials are designed to collect outcomes at or around pre-specified times after randomization. If there is variability in the times when participants are actually assessed, this can pose a challenge to learning the effect of treatment,…

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…

Statistics Theory · Mathematics 2023-03-23 Koulik Khamaru , Yash Deshpande , Tor Lattimore , Lester Mackey , Martin J. Wainwright

We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…

Numerical Analysis · Mathematics 2013-09-10 Yifeng Xu , Jun Zou

For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in…

Statistics Theory · Mathematics 2023-07-19 Miljenko Huzak , Snježana Lubura Strunjak , Andreja Vlahek Štrok

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating a unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk, i.e.…

Statistics Theory · Mathematics 2008-10-08 Leonid Galtchouk , Serguey Pergamenshchikov

We consider a diffusion $(\xi_t)_{t\ge 0}$ whose drift contains some deterministic periodic signal. Its shape being fixed and known, up to scaling in time, the periodicity of the signal is the unknown parameter $\vartheta$ of interest. We…

Statistics Theory · Mathematics 2010-10-26 Reinhard Hoepfner , Yury Kutoyants

We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…

Econometrics · Economics 2020-05-08 Ruijun Bu , Kaddour Hadri , Dennis Kristensen

With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…

Statistics Theory · Mathematics 2020-10-27 Jiyanglin Li , Tao Li

We study the problem of parameters estimation in Indirect Observability contexts, where $X_t \in R^r$ is an unobservable stationary process parametrized by a vector of unknown parameters and all observable data are generated by an…

Probability · Mathematics 2016-01-20 Robert Azencott , Peng Ren , Ilya Timofeyev

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…

Statistics Theory · Mathematics 2018-09-06 Jean Jacod , Michael Sørensen

Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity…

Statistics Theory · Mathematics 2020-11-13 Antoine Ayache , Myriam Fradon , Ravindi Nanayakkara , Andriy Olenko