Title: Asymptotic Properties of Recursive Maximum Likelihood Estimation in Non-Linear State-Space Models,
Abstract: Using stochastic gradient search and the optimal filter derivative, it is
possible to perform recursive (i.e., online) 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, Doucet and Singh, Biometrika 2018], a recursive
maximum likelihood algorithm based on a particle approximation to the optimal
filter derivative has been proposed and studied through numerical simulations.
Here, this algorithm and its asymptotic behavior are analyzed theoretically. We
show that the algorithm accurately estimates maxima to the underlying (average)
log-likelihood when the number of particles is sufficiently large. We also
derive (relatively) tight bounds on the estimation error. The obtained results
hold under (relatively) mild conditions and cover several classes of non-linear
state-space models met in practice.