Related papers: A Rademacher-Menchov approach for random coefficie…

This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…

In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean…

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…

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify…

We investigate the estimation of parameters in the random coefficient autoregressive model. We consider a nonstationary RCA process and show that the innovation variance parameter cannot be estimated by the quasi-maximum likelihood method.…

We study the behavior of the Riemann zeta function on the critical line when the imaginary part of the argument is sampled by the Cauchy random walk. We develop a complete second order theory for the corresponding system of random variables…

The random coefficient integer-valued autoregressive process was introduced by Zheng, Basawa, and Datta. In this paper we study the asymptotic behavior of this model (in particular, weak limits of extreme values and the growth rate of…

This paper is devoted to two different two-time-scale stochastic approximation algorithms for superquantile estimation. We shall investigate the asymptotic behavior of a Robbins-Monro estimator and its convexified version. Our main…

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step…

This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…

In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…

We study asymptotic behavior of conditional least squares estimators for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration based on discrete time (low frequency)…

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…

We propose some backward-forward martingale decompositions for functions of reversible Markov chains. These decompositions are used to prove the functional CLT for reversible Markov chains with asymptotically linear variance of partial…