  State space models (SSMs) are now ubiquitous in many fields and increasingly
complicated with observed and unobserved variables often interacting in
non-linear fashions. The crucial task of validating model assumptions thus
becomes difficult, particularly since some assumptions are formulated about
unobserved states and thus cannot be checked with data. Motivated by the
complex SSMs used for the assessment of fish stocks, we introduce a robust
estimation method for SSMs. We prove the Fisher consistency of our estimator
and propose an implementation based on automatic differentiation and the
Laplace approximation of integrals which yields fast computations. Simulation
studies demonstrate that our robust procedure performs well both with and
without deviations from model assumptions. Applying it to the stock assessment
model for pollock in the North Sea highlights the ability of our procedure to
identify years with atypical observations.

Methodology