Asymptotic properties of recursive particle maximum likelihood estimation
Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. I...
| Main Authors: | , |
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| פורמט: | Journal article |
| שפה: | English |
| יצא לאור: |
IEEE
2020
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| סיכום: | Using stochastic gradient search and the optimal filter derivative, it is possible to perform
recursive maximum likelihood estimation in a non-linear state-space model. As the optimal filter and
its derivative are analytically intractable for such a model, they need to be approximated numerically.
In [25], a recursive maximum likelihood algorithm based on a particle approximation to the optimal
filter derivative has been proposed and studied through numerical simulations. This algorithm and its
asymptotic behavior are here analyzed theoretically. Under regularity conditions, we show that the
algorithm accurately estimates maxima of the underlying (average) log-likelihood when the number
of particles is sufficiently large. We also provide qualitative upper bounds on the estimation error in
terms of the number of particles. |
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