2019
Том 71
№ 10

# Ivanov O. V.

Articles: 12
Article (Ukrainian)

### 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.

Article (Ukrainian)

### 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.

Article (Ukrainian)

### 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.

Article (Ukrainian)

### 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.

Article (Ukrainian)

### Asymptotic normality of M-estimates in the classical nonlinear regression model

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.

Article (Russian)

### Asymptotic expansions associated with the jackknife functional. II

Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 731–736

This paper is a sequel to part I [Ukr. Mat. Zh.,47, No. 4, 443–452 (1995)]. By using the results of the first part, we obtain the initial terms of the asymptotic expansions of the bias and variance for the jackknife estimator of the variance of the error of observations in a nonlinear regressive model.

Article (Russian)

### Asymptotic expansions associated with the jackknife functional. I

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.

Article (English)

### 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

Representable in the form $\mathcal{H}_B \bigcap G$, where $G = C(M(H^{\infty})) \overset{\rm def}{=} \text{alg}(H^{\infty}, \overline{H^{\infty}})$ and $\mathcal{H}_B$ is a closed subalgebra in $C(D)$ consisting of the functions that have nontangential limits almost everywhere on $\mathbb{T}$, and these limits belong to the Douglas algebra $B$. In this paper we describe the space $M(\mathcal{H}^G_B)$ of maximal ideals of the algebra $\mathcal{H}^G_B$ and prove that $M(\mathcal{H}^G_B) = M(B) \bigcup M(\mathcal{H}^G_0)$ and prove that $M(\mathcal{H}^G_0)$, where $\mathcal{H}^G_0$ is a closed ideal in $G$ consisting of functions having nontangential limits equal to zero almost everywhere on $\mathbb{T}$. Moreover, it is established that $H^{\infty \supset } [\overline Z ] \ne \mathcal{H}_{H^\infty + C}^G$ on the disk. The Chang-Marshall theorem is generalized for the Banach algebras $\mathcal{H}^G_B$. We also prove that $\mathcal{H}^G_B = {\rm alg}(\mathcal{H}^G_{H^{\infty}}, \overline{IB})$ for any Douglas algebra $B$, where $IB = \{u_{\alpha}\}_B$ are inner functions such that $\overline{u_{\alpha}} \in B$ on $\mathbb{T}$.

Article (Ukrainian)

### Generalized analytic functions and analytic subalgebras

Ukr. Mat. Zh. - 1990. - 42, № 5. - pp. 616–620

Article (Ukrainian)

### Some remarks on the Bohr compactification of the number line

Ukr. Mat. Zh. - 1986. - 38, № 2. - pp. 154–158

Article (Ukrainian)

### A theorem of I. M. Gel'fand

Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 89—90

Article (Ukrainian)

### Topological properties of a certain bicompact extension satisfying the first countability axiom

Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 765—770