Physical Sciences and Mathematics Commons^™

Asymptotic Results For Empirical Processes In Informative Model Of Random Censorship From Both Sides, Abdurakhim Abdushukurov, Dilshod Mansurov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper, the empirical process in informative model of random censorship from both sides is investigated. For it, the limit Gaussian process with mean zero is founded. Under investigating of empirical process, the characterization properties of the considered informative model is used. The properties of the semiparametric estimator by using methods of numerical modeling are discussed.

Limit Theorems For Weakly Dependent Random Variables With Values In Stable Type P Banach Spaces, Olimjon Sharipov, Utkir Kobilov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We consider stable type p Banach spaces. We extend results known for independent random variables to the mixing random variables.

In particular we prove moment in equalities, low of large numbers and almost sure convergence of the series in the case of mixing random variables.

On Extensions And Restrictions Of Τ-Smooth And Τ-Maxitive Idempotent Measures, Muzaffar Eshimbetov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the paper we investigate maps between idempotent measures spaces, τ-maxitive idempotent measures and their extensions and restrictions. For an idempotent measure we prove that its extension is τ-maxitive if and only if its restriction is τ-maxitive.

Test Statistics Based On Independence Processes, Leyla Kakadjanova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Paper is devoted to investigating classical normalized empirical process of independence. Processes are investigated by using strong approximation methods with best rate of convergence. We also consider the problems of finding of limit distributions of certain classes of statistics for testing the hypothesis of independence of random variable and event. The application to random censoring model also considered.

Sequential Estimation By Intervals Of A Fixed Width Of The Asymptotic Variance Of Rank Estimates Of The Shift Parameter, Gulnoza Rakhimova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we consider a sequential interval estimation by intervals of a fixed width of the asymptotic variance of rank estimates of the shift parameter. Reviewed the asymptotical properties of estimates of functionals of an unknown probability density and the conditions of the asymptotical consistency of a confidence interval of a fixed width and the asymptotical efficiency of the stopping time. The convergence rate of consistency of the fixed width interval for the asymptotic variance of rank estimates of the shift parameter is obtained.

On The Asymptotic Behavior Of Branching Processes With Stationary Immigration, Yakubjan Khusanbaev, Sadulla Sharipov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we consider nearly critical branching processes with immigration. We study the convergence of a sequence of nearly critical branching processes with immigration when immigration is a stationary in wide sense. Moreover, we derive an asymptotic for characteristic function of this process.

The Optimal Risk Of Estimator Of Conditional Distribution Function In A Model Of Heteroscedastic Regression With Weakly Dependent Observations, Farkhad Abdikalikov, Laura Reymova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Paper is devoted to estimation of conditional distribution function in heteroscedastical regression model, in which responses are α-mixing random variables. It is found the expression for mean square deviation of estimator and optimal window width sequence.