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Estimation of graphical models for skew continuous data

Author

Listed:
  • Linh H. Nghiem
  • Francis K. C. Hui
  • Samuel Müller
  • Alan H. Welsh

Abstract

We consider a new approach for estimating non‐Gaussian undirected graphical models. Specifically, we model continuous data from a class of multivariate skewed distributions, whose conditional dependence structure depends on both a precision matrix and a shape vector. To estimate the graph, we propose a novel estimation method based on nodewise regression: we first fit a linear model, and then fit a one component projection pursuit regression model to the residuals obtained from the linear model, and finally threshold appropriate quantities. Theoretically, we establish error bounds for each nodewise regression and prove the consistency of the estimated graph when the number of variables diverges with the sample size. Simulation results demonstrate the strong finite sample performance of our new method over existing methods for estimating Gaussian and non‐Gaussian graphical models. Finally, we demonstrate an application of the proposed method on observations of physicochemical properties of wine.

Suggested Citation

  • Linh H. Nghiem & Francis K. C. Hui & Samuel Müller & Alan H. Welsh, 2022. "Estimation of graphical models for skew continuous data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1811-1841, December.
  • Handle: RePEc:bla:scjsta:v:49:y:2022:i:4:p:1811-1841
    DOI: 10.1111/sjos.12569
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    References listed on IDEAS

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