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An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum…

Statistics Theory · Mathematics 2007-06-13 Randal Douc , Eric Moulines , Tobias Ryden

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

Statistics Theory · Mathematics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper (2007) for estimation of unknown nonparametric regression. We prove that this procedure is asymptotically efficient for a quadratic risk. It…

Statistics Theory · Mathematics 2008-12-18 Leonid Galtchouk , Serguey Pergamenshchikov

We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…

Statistics Theory · Mathematics 2020-03-12 Niko Lietzén , Lauri Viitasaari , Pauliina Ilmonen

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…

Statistics Theory · Mathematics 2024-06-06 Yuliya Mishura , Kostiantyn Ralchenko , Olena Dehtiar

By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to…

Statistics Theory · Mathematics 2011-07-20 Nils Lid Hjort , David Pollard

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 paper deals with the asymptotic laws of functional of standard random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain…

Methodology · Statistics 2016-11-22 Gane Samb Lo , Adja Mbarka Fall , Cheikhna Hamallah Ndiaye , Akym Adekpejou

In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…

Applications · Statistics 2016-12-13 Maryam Sohrabi , Mahmoud Zarepour

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

Statistics Theory · Mathematics 2016-11-22 Teo Sharia , Lei Zhong

This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…

Probability · Mathematics 2024-10-04 Michael Levine , Xiaoguang Wang , Jian Frank Zou

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…

Statistics Theory · Mathematics 2015-12-29 Teppei Ogihara

We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is…

Statistics Theory · Mathematics 2011-05-12 Markus Reiß

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…

Statistics Theory · Mathematics 2014-06-17 Matyas Barczy , Leif Doering , Zenghu Li , Gyula Pap

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of autoregressive moving-average (ARMA) models with regime changes under the assumption that the errors are uncorrelated but not necessarily independent.…

Statistics Theory · Mathematics 2019-07-11 Yacouba Boubacar Maïnassara , Landy Rabehasaina

This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the…

Statistics Theory · Mathematics 2011-04-28 T. Yoshida , K. Naito

In this article we focus on estimating the quadratic covariation of continuous semimartingales from discrete observations that take place at asynchronous observation times. The Hayashi-Yoshida estimator serves as synchronized realized…

Statistics Theory · Mathematics 2011-06-22 Markus Bibinger

First we provide a simple set of sufficient conditions for the weak convergence of scaled affine processes with state space $R_+ \times R^d$. We specialize our result to one-dimensional continuous state branching processes with immigration.…

Statistics Theory · Mathematics 2013-03-19 Matyas Barczy , Leif Doering , Zenghu Li , Gyula Pap

This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…

Statistics Theory · Mathematics 2023-05-18 Marie Badreau , Frédéric Proïa

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…

Machine Learning · Statistics 2020-05-26 Rodrigo A. González , Cristian R. Rojas