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

Guodong Shan, Yiheng Hou and Baisen Liu ()
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Guodong Shan: Changchun University
Yiheng Hou: Dongbei University of Finance and Economics
Baisen Liu: Dongbei University of Finance and Economics

Computational Statistics, 2020, vol. 35, issue 4, No 23, 2077-2092

Abstract: 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.

Keywords: Functional data; Outliers; Scale mixtures of normal distributions; Metropolis-Hastings (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00180-020-00975-3

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