State space models (SSMs) are now ubiquitous in many fields and increasingly complicated with observed and unobserved variables often interacting in nonlinear 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.

中文翻译：

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离散时间状态空间模型的稳健估计

状态空间模型 (SSM) 现在在许多领域中无处不在，并且随着观察到和未观察到的变量经常以非线性方式相互作用，变得越来越复杂。验证模型假设的关键任务因此变得困难，特别是因为一些假设是关于未观察到的状态，因此无法用数据检查。受用于评估鱼类种群的复杂 SSM 的启发，我们介绍了一种稳健的 SSM 估计方法。我们证明了我们的估计器的 Fisher 一致性，并提出了一种基于自动微分和积分的拉普拉斯近似的实现，从而产生快速计算。模拟研究表明，无论是否偏离模型假设，我们的稳健程序都表现良好。