9 citations · 25 across the 9 of their papers we have counts for
9 papers
Gaussian Volterra processes: asymptotic growth and statistical estimation
Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar
The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and t…
Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index
Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko +1
This paper is devoted to the study of the properties of entropy as a function of the Hurst index, which corresponds to the fractional Gaussian noise. Since the entropy of the Gauss…
Gaussian processes with Volterra kernels
Yuliya Mishura, Georgiy Shevchenko, Sergiy Shklyar
We study Volterra processes , where is a standard Wiener process, and the kernel has the form . This form gen…
Consistency of the total least squares estimator in the linear errors-in-variables regression
Sergiy Shklyar
This paper deals with a homoskedastic errors-in-variables linear regression model and properties of the total least squares (TLS) estimator. We partly revise the consistency result…
Parameter estimation for Gaussian processes with application to the model with two independent fractional Brownian motions
Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar
The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form , where $B…
Maximum likelihood drift estimation for Gaussian process with stationary increments
Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar
The paper deals with the regression model , , where is a centered Gaussian process with stationary increments. We study the estima…
Equivariant adjusted least squares estimator in two-line fitting model
Sergiy Shklyar
We consider the two-line fitting problem. True points lie on two straight lines and are observed with Gaussian perturbations. For each observed point, it is not known on which line…
Identifiability of logistic regression with homoscedastic error: Berkson model
Sergiy Shklyar
We consider the Berkson model of logistic regression with Gaussian and homoscedastic error in regressor. The measurement error variance can be either known or unknown. We deal with…
Approximation of fractional Brownian motion by martingales
Sergiy Shklyar, Georgiy Shevchenko, Yuliya Mishura +2
We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in…