Sokhadze G. A.
Ukr. Mat. Zh. - 2016. - 68, № 5. - pp. 586-600
We construct new criteria for the verification of the hypotheses that $p \geq 2$ independent samplings have identical densities of distributions (homogeneity hypothesis) or identically defined densities of distributions (compatibility hypothesis). We determine the ultimate powers of the constructed criteria for some local “close” alternatives.
Ukr. Mat. Zh. - 2015. - 67, № 4. - pp. 435-446
For integral functionals of the Gasser–Muller regression function and its derivatives, we consider the plug-in estimator. The consistency and asymptotic normality of the estimator are shown.
On the Square-Integrable Measure of the Divergence of Two Nuclear Estimations of the Bernoulli Regression Functions
Ukr. Mat. Zh. - 2015. - 67, № 1. - pp. 3–18
We establish the limit distribution of the square-integrable deviation of two nonparametric nuclear-type estimations for the Bernoulli regression functions. A criterion is proposed for the verification of the hypothesis of equality of two Bernoulli regression functions. We study the problem of verification and, for some “close” alternatives, investigate the asymptotics of the power.
Ukr. Mat. Zh. - 2010. - 62, № 12. - pp. 1642–1658
The problem of estimation of a distribution function is considered in the case where the observer has access only to a part of the indicator random values. Some basic asymptotic properties of the constructed estimates are studied. The limit theorems are proved for continuous functionals related to the estimation of $F^n(x)$ in the space $C[a,\; 1 - a], 0 < a < 1/2$.
On a measure of integral square deviation with generalized weight for the Rosenblatt–Parzen probability density estimator
Ukr. Mat. Zh. - 2010. - 62, № 4. - pp. 514–535
The limit distribution of an integral square deviation with weight in the form of “delta”-functions for the Rosenblatt–Parzen probability density estimator is determined. In addition, the limit power of the goodness-of-fit test constructed by using this deviation is investigated.
Ukr. Mat. Zh. - 1994. - 46, № 5. - pp. 586–596
Explicit filtration formulas are obtained for the solutions of nonlinear differential equations with random right-hand sides. In the case of a Gaussian random process, these formulas are simplified.