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Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions

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Abstract

Functional linear regression (FLR) is a popular method that studies the relationship between a scalar response and a functional predictor. A common estimation procedure for the FLR model is using maximum likelihood by assuming normal distributions for measurement errors; however this method may make inferences vulnerable to the presence of outliers. In this article, we introduce a robust estimation method of partially functional linear model by considering a class of scale mixtures of normal (SMN) distributions for measurement errors. Due to intractable closed form of likelihood function with the SMN distributions, a Bayesian framework is adopted and an MCMC algorithm is developed to carry out posterior inference on model parameters. The finite sample performance of our proposed method is evaluated by using some simulation studies and a real dataset.

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Acknowledgements

This work was supported by Department of Education of Liaoning Province (Grant Numbers LN2017ZD001).

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Authors and Affiliations

  1. School of Science, Changchun University, Changchun, 130002, China

    Guodong Shan

  2. School of Statistics, Dongbei University of Finance and Economics, Dalian, 116025, China

    Yiheng Hou & Baisen Liu

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  1. Guodong Shan
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  2. Yiheng Hou
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  3. Baisen Liu
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Correspondence to Baisen Liu.

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Shan, G., Hou, Y. & Liu, B. Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions. Comput Stat 35, 2077–2092 (2020). https://doi.org/10.1007/s00180-020-00975-3

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