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Robust Time-Varying Undirected Graphs

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Mauro Bernardi

    (University of Padova, Department of Statistical Sciences)

  • Paola Stolfi

    (Roma Tre University and Istituto per le Applicazioni del Calcolo “Mauro Picone” - CNR, Department of Economics)

Abstract

Undirected graphs are useful tools for the analysis of sparse and high-dimensional data sets. In this setting the sparsity helps in reducing the complexity of the model. However, sparse graphs are usually estimated under the Gaussian paradigm thereby leading to estimates that are very sensitive to the presence of outlying observations. In this paper we deal with sparse time-varying undirected graphs, namely sparse graphs whose structure evolves over time. Our contribution is to provide a robustification of these models, in particular we propose a robust estimator which minimises the γ-divergence. We provide an algorithm for the parameter estimation and we investigate the rate of convergence of the proposed estimator.

Suggested Citation

  • Mauro Bernardi & Paola Stolfi, 2018. "Robust Time-Varying Undirected Graphs," Springer Books, in: Marco Corazza & María Durbán & Aurea Grané & Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 117-120, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-89824-7_21
    DOI: 10.1007/978-3-319-89824-7_21
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