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We study the parameter estimation problem of Vasicek Model driven by sub-fractional Brownian processes from discrete observations, and let {S_t^H,t>=0} denote a sub-fractional Brownian motion whose Hurst parameter 1/2<H<1 . The studies are as follows: firstly, two unknown parameters in the model are estimated by the least squares method. Secondly, the strong consistency and the asymptotic distribution of the estimators are studied respectively. Finally, our estimators are validated by numerical simulation.
We consider a nonparametric version of the integer-valued GARCH(1,1) model for time series of counts. The link function in the recursion for the variances is not specified by finite-dimensional parameters, but we impose nonparametric smoothness condi
We study the problem of exact support recovery based on noisy observations and present Refined Least Squares (RLS). Given a set of noisy measurement $$ myvec{y} = myvec{X}myvec{theta}^* + myvec{omega},$$ and $myvec{X} in mathbb{R}^{N times D}$ which
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters
In a regression setting with response vector $mathbf{y} in mathbb{R}^n$ and given regressor vectors $mathbf{x}_1,ldots,mathbf{x}_p in mathbb{R}^n$, a typical question is to what extent $mathbf{y}$ is related to these regressor vectors, specifically,
In this paper, we consider an inference problem for the first order autoregressive process driven by a long memory stationary Gaussian process. Suppose that the covariance function of the noise can be expressed as $abs{k}^{2H-2}$ times a function slo