Robust MLE for stochastic state space model with observation outliers

The objective of this paper is to develop a robust maximum likelihood estimates (MLE) for the stochastic state space model via the expectation maximization (EM) algorithm to cope with observation outliers. Two types of outliers and their influence have been studied in this sequel namely the additive (AO) and innovative outliers (IO). Due to the sensitivity of the MLE to AO and IO we propose two techniques for robustifying the MLE: the weighted maximum likelihood estimate (WMLE) and the trimmed maximum likelihood estimate (TMLE). The WMLE is easy to implement, however it is still sensitive to IO. On the other hand, the TMLE is a combinatorial optimization problem and hard to implement but it is efficient to all types of outliers presented here. A Monte Carlo simulation result shows the efficiency of of the TMLE and WMLE based on the EM algorithm.