A sequential Monte Carlo Gibbs coupled with stochastically approximated expectation-maximization algorithm for functional data

We develop an algorithm to overcome the curse of dimensionality in sequential Monte Carlo (SMC) for functional data. In the inner iterations of the algorithm for given parameter values, the conditional SMC is extended to obtain draws of the underlying state vectors. These draws in turn are used in the outer iterations to update the parameter values in the framework of stochastically approximated expectation-maximization to obtain maximum likelihood estimates of the parameters. Standard errors of the parameters are calculated using a stochastic approximation of Louis formula. Three numeric examples are used for illustration. They show that although the computational burden remains high, the algorithm produces reasonable results without exponentially increasing the particle numbers.

Keywords

functional data, Gibbs sampler, particle filter, sequential Monte Carlo, state space model, stochastically approximated EM

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Received 24 February 2020

Accepted 11 December 2020

Published 11 January 2022