Ivanov O. V.
Asymptotic properties of $M$-estimates of parameters in a nonlinear regression model with discrete time and singular spectrum
Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 28-51
We study a nonlinear regression model with discrete time and observations errors whose spectrum is singular. Sufficient conditions are obtained for the consistency, asymptotic uniqueness and asymptotic normality of the $M$-estimates of the unknown parameters.
On the Whittle Estimator of the Parameter of Spectral Density of Random Noise in the Nonlinear Regression Model
Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1050-1067
We consider a nonlinear regression model with continuous time and establish the consistency and asymptotic normality of the Whittle minimum contrast estimator for the parameter of spectral density of stationary Gaussian noise.
Asymptotic Expansion of the Moments of Correlogram Estimator for the Random-Noise Covariance Function in the Nonlinear Regression Model
Ukr. Mat. Zh. - 2014. - 66, № 6. - pp. 787–805
We establish asymptotic expansions of the bias, mean-square deviation, and variance for the correlogram estimator of the unknown covariance function of a Gaussian stationary random noise in the nonlinear regression model with continuous time.
On the asymptotic distribution of the Koenker?Bassett estimator for a parameter of the nonlinear model of regression with strongly dependent noise
Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1030-1052
We prove that, under certain regularity conditions, the asymptotic distribution of the Koenker - Bassett estimator coincides with the asymptotic distribution of the integral of the indicator process generated by a random noise weighted by the gradient of the regression function.
Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1470–1488
Sufficient conditions are obtained for the asymptotic normality of M-estimates of the unknown parameters of nonlinear regression models with discrete time and independent identically distributed errors of observations.
Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 443–451
We obtain an asymptotic expansion of the functional of the jackknife method, which is used for the estimation of the variance of observational errors in a nonlinear regression model.
The structure of Banach algebras of bounded continuous functions on the open disk that contain H?, the Hoffman algebra, and nontangential limits
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 924–931
Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 616–620
Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 154–158
Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 89—90
Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 765—770