On large deviations in estimation problem with dependent observations
The paper is devoted to the stochastic optimization problem with a stationary ergodic random sequence satisfying the hypermixing condition. It is assumed that we have the finite number of observed elements in the sequence, and instead of solving the former problem we investigate the empirical func...
Збережено в:
| Дата: | 2005 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2005
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| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/4430 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On large deviations in estimation problem with dependent observations / P.S. Knopov, E.J. Kasitskaya // Theory of Stochastic Processes. — 2005. — Т. 11 (27), № 3-4. — С. 97–103. — Бібліогр.: 4 назв.— англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The paper is devoted to the stochastic optimization problem with a stationary ergodic
random sequence satisfying the hypermixing condition. It is assumed that we have
the finite number of observed elements in the sequence, and instead of solving the
former problem we investigate the empirical function, find its points of minimum,
and study their asymptotic properties. More precisely we consider the probabilities
of large deviations of minimizers and the minimal value of the empirical criterion
function from the corresponding characteristics of the main problem. The conditions
under which the probabilities of the large deviations decrease exponentially are found. |
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