2019
Том 71
№ 11

# Maiboroda R. E.

Articles: 10
Article (Ukrainian)

### Estimate for Euclidean parameters of a mixture of two symmetric distributions

Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 945–953

A sample from a mixture of two symmetric distributions is observed. The considered distributions differ only by a shift. Estimates are constructed by the method of estimating equations for parameters of mean locations and concentrations (mixing probabilities) of both components. We obtain conditions for the asymptotic normality of these estimates. The greatest lower bounds for the coefficients of dispersion of the estimates are determined.

Article (Ukrainian)

### A Test for the Homogeneity of Mixtures with Varying Concentrations

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1097-1102

We construct a generalized version of the Kolmogorov–Smirnov test for the verification of a hypothesis concerning the homogeneity of a sample against an alternative sample from a mixture with varying concentrations. We obtain asymptotic formulas and nonasymptotic upper bounds for the probabilities of errors of the first and second kinds.

Article (Russian)

### Asymptotic normality and efficiency of a weighted correlogram

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 937–947

For a process X(t)=Σ j=1 M g j (t j (), where gj(t) are nonrandom given functions, $(\xi _j (t),j = \overline {1,M} )$ is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate $\hat r_{kl} (\tau ,T)$ for the functions r kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of $\sqrt T (\hat r_{kl} (\tau ,T) - r_{kl} (\tau ))$ as T → ∞. We consider the problem of the optimal choice of parameters of the estimate $\hat r_{kl}$ depending on observations.

Brief Communications (Ukrainian)

### Estimates for distributions of components of mixtures with varying concentrations

Ukr. Mat. Zh. - 1996. - 48, № 4. - pp. 558-562

For the data of sampling from a mixture of several components with varying concentrations, we construct nonparametric estimates for the distributions of components and determine the rank correlation coefficient. We prove the consistency of the rank coefficient and the efficiency of the estimates of distributions.

Article (Russian)

### Estimates of intense noise for inhomogeneous diffusion processes

Ukr. Mat. Zh. - 1995. - 47, № 7. - pp. 946–951

Nonparametric estimates of noise intensityg(t) are obtained. These estimates are constructed for datax(t) defined by the equationdx(t)=f(x(t),t)dt+g(t)dw(t). The validity of the estimates is proved.

Article (Russian)

### Estimation of the discord time for a process of the Ornstein-Uhlenbeck type

Ukr. Mat. Zh. - 1993. - 45, № 9. - pp. 1198–1204

A consistent estimate is constructed for the discord time of a process of the Ornstein-Uhlenbeck type. The rate of the almost sure convergence of this estimate is investigated and the confidence interval is determined.

Article (Ukrainian)

### Nonparametric detection of change points from observations with errors

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 706-709

Article (Ukrainian)

### Asymptotic behavior of empirical generating moment functions of random variables

Ukr. Mat. Zh. - 1989. - 41, № 7. - pp. 992-994

Article (Ukrainian)

### Estimates for the moment-generating function for stationary random processes

Ukr. Mat. Zh. - 1986. - 38, № 4. - pp. 504-509