Моделювання зіткнення літаків з використанням методики істотних вибірок

We introduce the model of movement of two conflicting aircrafts and state the problem, we apply the importance sampling technique and elaborate an algorithm of collision modeling based on normal distributions, a small simulation studyРассмотрена модель движения двух конфликтующих самолетов. Предложены методика важных выборок и алгоритм моделирования столкновения самолетов, основанный на нормальном распределенииРозглянуто модель руху двох конфліктуючих літаків. Запропоновано методику істотних вибірок і алгоритм моделювання зіткнення літаків, заснований на нормальному розподіл

Goodness-of-Fit Test in a Structural Errors-in-Variables Model Based on the Quasi-Likelihood Estimator

A polynomial structural measurement error model is considered. A goodnessof- fit test is constructed based on the quasi-likelihood estimator, which is asymptotically optimal in a large class of estimators. The power of the test is discussed. The test for the linear model is studied in more detail. Similar test can be applied to much more general situation, where the estimator is constructed by optimization or score equations

Goodness-of-Fit Test in a Structural Errors-in-Variables Model Based on the Quasi-Likelihood Estimator

A polynomial structural measurement error model is considered. A goodnessof- fit test is constructed based on the quasi-likelihood estimator, which is asymptotically optimal in a large class of estimators. The power of the test is discussed. The test for the linear model is studied in more detail. Similar test can be applied to much more general situation, where the estimator is constructed by optimization or score equations

Estimation of correct recognition probability by Bayes’ equation in case of not precisely known distribution density

A procedure of estimation of correct recognition probability by Bayes’ equation in the case of not precisely known distribution density is suggested. Expression for error estimation considering inaccuracy of determination of distribution density is obtained. Variants of estimation of correct recognition probability for different sample volumes are resulted

Ellipse Fitting with Hyperaccuracy

Abstract. For fitting an ellipse to a point sequence, ML (maximum likelihood) has been regarded as having the highest accuracy. In this paper, we demonstrate the existence of a “hyperaccurate ” method which outperforms ML. This is made possible by error analysis of ML followed by subtraction of high-order bias terms. Since ML nearly achieves the theoretical accuracy bound (the KCR lower bound), the resulting improvement is very small. Nevertheless, our analysis has theoretical significance, illuminating the relationship between ML and the KCR lower bound.