Abstract State–space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state–space model is specified through a parametric model. However, the specification of such a parametric model may require an important modeling effort or may lead to models which are not flexible enough to reproduce all the complexity of the phenomenon of interest. In such situations, an appealing alternative consists in inferring the state–space model directly from the data using a non-parametric framework. The recent developments of powerful simulation techniques have permitted to improve the statistical inference for parametric state–space models. It is proposed to combine two of these techniques, namely the Stochastic Expectation–Maximization (SEM) algorithm and Sequential Monte Carlo (SMC) approaches, for non-parametric estimation in state–space models. The performance of the proposed algorithm is assessed though simulations on toy models and an application to environmental data is discussed.

中文翻译：

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状态空间模型中的非参数估计算法

摘要 状态空间模型在统计文献中无处不在，因为它们为分析许多时间序列提供了灵活且可解释的框架。在大多数实际应用中，状态空间模型是通过参数模型指定的。然而，这种参数模型的规范可能需要重要的建模工作，或者可能导致模型不够灵活，无法重现感兴趣现象的所有复杂性。在这种情况下，一个有吸引力的替代方案是使用非参数框架直接从数据中推断出状态空间模型。强大的仿真技术的最新发展已经允许改进参数状态空间模型的统计推断。建议结合这两种技术，即随机期望最大化（SEM）算法和顺序蒙特卡罗（SMC）方法，用于状态空间模型中的非参数估计。通过对玩具模型的模拟评估了所提出算法的性能，并讨论了对环境数据的应用。