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Partially linear models based on heavy-tailed and asymmetrical distributions

Abstract

In this paper, we provide an extension for partially linear models (PLMs) to allow the errors to follow a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric as well as lightly/heavily tailed distributions which can be used to model datasets with outlying and also atypical data. Using a suitable hierarchical representation of the TP-SMN family developed specifically for PLM, we derived an EM-type algorithm for iteratively computing maximum penalized likelihood estimates of the proposed model parameters. We examined the performance of the proposed PLM model and methodology using simulation studies and a real dataset to show the robust aspects of this model.

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Authors

Contributions

MB: data curation, validation, writing—original draft. KZ: conceptualization, writing, software, supervision. MM: investigation, methodology, software, review & editing. ZK: visualization, review and editing.

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Correspondence to Karim Zare.

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The authors declare that they have no conflict of interest.

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Bazrafkan, M., Zare, K., Maleki, M. et al. Partially linear models based on heavy-tailed and asymmetrical distributions. Stoch Environ Res Risk Assess (2021). https://doi.org/10.1007/s00477-021-02101-1

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Keywords

  • ECME algorithm
  • Partially linear model
  • Two-piece scale mixtures of normal distributions