An algorithm for non-parametric estimation in state–space models

• Published in: Computational statistics & data analysis Vol. 153; p. 107062
• Main Authors: Chau, Thi Tuyet Trang, Ailliot, Pierre, Monbet, Valérie
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2021; Elsevier
• Subjects: algorithms; Conditional particle filter; Continental interfaces, environment; estimation; lead; literature; Local linear regression; methodology; Non-parametric statistics; Ocean, Atmosphere; Sciences of the Universe; SEM algorithm; State–space models; statistical inference; time series analysis; Conditional particle filter; State–space models; Non-parametric statistics; Local linear regression; SEM algorithm
• ISSN: 0167-9473; 1872-7352; 1872-7352
• DOI: 10.1016/j.csda.2020.107062

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.