Estimation and testing of a small change location in the intensity of a Poisson process S. Dachian, L. Yang
Material type:
ArticleOther title: Оценивание и проверка гипотезы о малых изменениях интенсивности пуассоновского процесса [Parallel title]Subject(s): Пуассона процесс | точка изменения | малый скачок | статистическое оценивание | проверка гипотезGenre/Form: статьи в сборниках Online resources: Click here to access online
In:
Международная научная конференция "Робастная статистика и финансовая математика - 2018" 09-11 июля 2018 г. : сборник статей С. 22-30Abstract: A model of Poissonian observations having a jump (changepoint)
in the intensity function is considered in the case when
the size of the jump converges to zero. The limiting likelihood
ratio in this case is quite different from the one corresponding
to the case of a fixed jump-size. More precisely, we show that
the limiting likelihood ratio is a log-Wiener process, and so, this
model is asymptotically equivalent to the well known model of a
signal in white Gaussian noise. Further, we deduce the properties
of the maximum likelihood and Bayesian estimators, as well
as those of the general likelihood ratio, Wald’s and two Bayesian
tests. We illustrate the results by numerical simulations.
Библиогр.: 6 назв.
A model of Poissonian observations having a jump (changepoint)
in the intensity function is considered in the case when
the size of the jump converges to zero. The limiting likelihood
ratio in this case is quite different from the one corresponding
to the case of a fixed jump-size. More precisely, we show that
the limiting likelihood ratio is a log-Wiener process, and so, this
model is asymptotically equivalent to the well known model of a
signal in white Gaussian noise. Further, we deduce the properties
of the maximum likelihood and Bayesian estimators, as well
as those of the general likelihood ratio, Wald’s and two Bayesian
tests. We illustrate the results by numerical simulations.
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