Abstract:
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In the state-space modeling framework, parameter estimation is often accomplished by maximizing the innovations Gaussian log-likelihood. The maximum likelihood estimator (MLE) is efficient when the normality assumption is satisfied. However, in the presence of contamination or thicker-tailed noise distributions, the MLE suffers from a lack of robustness. Basu, Harris, Hjort, and Jones (1998) introduced a discrepancy measure (BHHJ) with a nonnegative tuning parameter that controls the trade-off between robustness and efficiency. In this talk, we propose a new parameter estimation procedure based on the BHHJ discrepancy for fitting state-space models. As the tuning parameter is increased, the estimation procedure becomes more robust but less efficient. We investigate the performance of the procedure in a comprehensive simulation study. In addition, we provide guidelines on how to choose an appropriate tuning parameter in practice.
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