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We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the…

Probability · Mathematics 2015-03-17 Antoine Lejay , Ernesto Mordecki , Soledad Torres

We propose estimators for the parameters of the Linnik L$(\alpha,\gamma)$ distribution. The estimators are derived from the moments of the log-transformed Linnik distributed random variable, and are shown to be asymptotically unbiased. The…

Methodology · Statistics 2017-03-27 Dexter Cahoy

We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…

Statistics Theory · Mathematics 2009-09-29 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

Non-parametric estimation of a convex discrete distribution may be of interest in several applications, such as the estimation of species abundance distribution in ecology. In this paper we study the least squares estimator of a discrete…

Methodology · Statistics 2012-02-29 Cécile Durot , François Koladjo , Sylvie Huet , Stéphane Robin

This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…

Statistics Theory · Mathematics 2026-04-24 Vladimir Pastukhov

In this paper, we consider a least-squares (LS)-based distributed algorithm build on a sensor network to estimate an unknown parameter vector of a dynamical system, where each sensor in the network has partial information only but is…

Systems and Control · Electrical Eng. & Systems 2022-12-19 Siyu Xie , Yaqi Zhang , Lei Guo

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

Computation · Statistics 2018-11-06 J. Martin van Zyl

We consider the problem of inference for projection parameters in linear regression with increasing dimensions. This problem has been studied under a variety of assumptions in the literature. The classical asymptotic normality result for…

Statistics Theory · Mathematics 2024-01-12 Woonyoung Chang , Arun Kumar Kuchibhotla , Alessandro Rinaldo

We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new…

Statistics Theory · Mathematics 2015-12-29 Yohann De Castro , Élisabeth Gassiat , Claire Lacour

We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For…

Probability · Mathematics 2017-07-27 Beáta Bolyog , Gyula Pap

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…

Methodology · Statistics 2007-12-25 Fabienne Comte , Valentine Genon-Catalot , Yves Rozenholc

We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew…

Probability · Mathematics 2017-01-10 Antoine Lejay , Paolo Pigato

In this paper, we give a tutorial on asymptotic properties of the Least Square (LS) and Regularized Least Squares (RLS) estimators for the finite impulse response model with filtered white noise inputs. We provide three perspectives: the…

Statistics Theory · Mathematics 2022-01-03 Yue Ju , Tianshi Chen , Biqiang Mu , Lennart Ljung

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…

Statistics Theory · Mathematics 2018-11-06 Dragi Anevski , Vladimir Pastukhov

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…

Probability · Mathematics 2009-06-29 Bernard Bercu , Benoite de Saporta , Anne Gegout-Petit

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…

Methodology · Statistics 2015-12-09 James Robins , Lingling Li , Eric Tchetgen Tchetgen , Aad van der Vaart

The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…

Probability · Mathematics 2015-03-20 Vassili Blandin

Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…

Statistics Theory · Mathematics 2016-10-20 Alan Muro , Sara van de Geer

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

It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…

Statistics Theory · Mathematics 2010-06-09 Radhendushka Srivastava , Debasis Sengupta