arXiv subjects
Publications and source records attributed to Alexander V. Ivanov.
A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are obtained.
In this paper, the estimation of parameters in the harmonic regression with cyclically dependent errors is addressed. Asymptotic properties of the least-squares estimates are analyzed by simulation experiments. By numerical simulation, we prove that consistency and asymptotic normality of the least-squares parameter estimator studied holds under different scenarios, where theoretical results do not exist, and have yet to be proven. In particular, these two asymptotic properties are shown by simulations for the least-squares parameter estimator in the non-linear regression model analyzed, when its error term is defined as a non-linear transformation of a Gaussian random process displaying long-range dependence.
The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.