Model selection for the robust efficient signal processing observed with small Lévy noise S. Beltaief, O. V. Chernoyarov, S. M. Pergamenshchikov
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ArticleContent type: Текст Media type: электронный Subject(s): неасимптотическое оценивание | обработка сигналов | Леви шумы | оракульные неравенстваGenre/Form: статьи в журналах Online resources: Click here to access online
In:
Annals of the Institute of Statistical Mathematics Vol. 72, № 5. P. 1205-1235Abstract: We develop a new model selection method for an adaptive robust efficient nonparametric
signal estimation observed with impulse noise which is defined by a general
non-Gaussian Lévy process. On the basis of the developed method, we construct
estimation procedures which are analyzed in two settings: in non-asymptotic and in
asymptotic ones. For the first time for such models, we show non-asymptotic sharp
oracle inequalities for quadratic and robust risks, i.e., we show that the constructed
procedures are optimal in the sense of sharp oracle inequalities. Next, bymaking use of
the obtained oracle inequalities, we provide an asymptotic efficiency property for the
developed estimation methods in an adaptive setting when the signal/noise ratio goes
to infinity. We apply the developed model selection methods for the signal number
detection problem in multi-path information transmission.
Библиогр.: с. 1233-1234
We develop a new model selection method for an adaptive robust efficient nonparametric
signal estimation observed with impulse noise which is defined by a general
non-Gaussian Lévy process. On the basis of the developed method, we construct
estimation procedures which are analyzed in two settings: in non-asymptotic and in
asymptotic ones. For the first time for such models, we show non-asymptotic sharp
oracle inequalities for quadratic and robust risks, i.e., we show that the constructed
procedures are optimal in the sense of sharp oracle inequalities. Next, bymaking use of
the obtained oracle inequalities, we provide an asymptotic efficiency property for the
developed estimation methods in an adaptive setting when the signal/noise ratio goes
to infinity. We apply the developed model selection methods for the signal number
detection problem in multi-path information transmission.
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