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.

中文翻译：

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使用重尾分布的部分函数线性回归模型的贝叶斯鲁棒估计

功能线性回归（FLR）是研究标量响应与功能预测变量之间关系的一种流行方法。FLR模型的常见估算程序是通过假设测量误差的正态分布来使用最大似然。但是，此方法可能会使推断容易受到异常值的影响。在本文中，我们通过考虑测量误差的正态（SMN）分布的比例混合类别，介绍了一种部分函数线性模型的鲁棒估计方法。由于具有SMN分布的似然函数的不可压缩闭合形式，因此采用了贝叶斯框架，并开发了MCMC算法对模型参数进行后验推断。