Asymptotic properties of recursive particle maximum likelihood estimation
| Autor: | Arnaud Doucet, Vladislav B. Tadić |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Maximum likelihood
Recursive maximum likelihood Sequential monte carlo methods Markov process 02 engineering and technology Derivative Library and Information Sciences 01 natural sciences 010104 statistics & probability symbols.namesake Convergence (routing) 0202 electrical engineering electronic engineering information engineering Applied mathematics 0101 mathematics Hidden Markov model Mathematics 010102 general mathematics System identification Approximation algorithm 020206 networking & telecommunications Filter (signal processing) Statistics::Computation Computer Science Applications Filter (video) Kernel (statistics) symbols Particle Maxima Information Systems |
| Zdroj: | ISIT |
| Popis: | 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 Poyiadjis et al. (G. Poyiadjis, A. Doucet, and S. S. Singh, Biometrika, vol. 98, no. 1, pp. 65–80, 2011), 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 log-likelihood rate 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|