On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters

A multivariate trigonometric regression model is considered. Various discrete modifications of the similar bivariate model received serious attention in the literature on signal and image processing due to multiple applications in the analysis of symmetric textured surfaces. In the paper asymptotic normality of the least squares estimator for amplitudes and angular frequencies is obtained in multivariate trigonometric model assuming that the random noise is a homogeneous or homogeneous and isotropic Gaussian, in particular, strongly dependent random field on R M , M > 2. \mathbb {R}^M,\,\, M>2.

On the generalization of the central limit theorem for the least-squares estimator of the unknown parameter in the autoregressive process of order one (AR(1))

In this work it is proved central limit theorem for the least-squares estimator of the unknown parameter in the generalization autoregressive process of order one (AR(1)).

Least squares estimator for stochastic differential equations driven by small fractional Lévy noises from discrete observations

In this paper, we consider the problem of parameter estimation for stochastic differential equations with small fractional Lévy noises, based on discrete observations. Under certain regularity conditions on drift function, the consistency of least squares estimation has been established as a small dispersion coefficient [Formula: see text] and the number of discrete points [Formula: see text] simultaneously. We also obtain the asymptotic behavior of the estimator.