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. 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. [ABSTRACT FROM AUTHOR]