This paper focuses on the problems of estimation and variable selection in the functional linear regression model (FLM) with functional response and scalar covariates. To this end, two different types of regularization (L1 and L2 ) are considered in this paper. On the one hand, a sample approach for functional LASSO in terms of basis representation of the sample values of the response variable is proposed. On the other hand, we propose a penalized version of the FLM by introducing a P-spline penalty in the least squares fitting criterion. But our aim is to propose P-splines as a powerful tool simultaneously for variable selection and functional parameters estimation. In that sense, the importance of smoothing the response variable before fitting the model is also studied. In summary, penalized (L1 and L2 ) and nonpenalized regression are combined with a presmoothing of the response variable sample curves, based on regression splines or P-splines, providing a total of six approaches to be compared in two simulation schemes. Finally, the most competitive approach is applied to a real data set based on the graft-versus-host disease, which is one of the most frequent complications (30% -50%) in allogeneic hematopoietic stem-cell transplantation.

中文翻译：

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函数线性回归中的 P 样条变量选择：在移植物抗宿主病中的应用

本文重点研究具有函数响应和标量协变量的函数线性回归模型（FLM）中的估计和变量选择问题。为此，本文考虑了两种不同类型的正则化（L1 和 L2）。一方面，在响应变量的样本值的基础表示方面，提出了泛函LASSO的样本方法。另一方面，我们通过在最小二乘拟合标准中引入 P 样条惩罚来提出 FLM 的惩罚版本。但我们的目标是提出 P 样条作为同时用于变量选择和功能参数估计的强大工具。从这个意义上说，还研究了在拟合模型之前平滑响应变量的重要性。总之，惩罚（L1 和 L2 ）和非惩罚回归与响应变量样本曲线的预平滑相结合，基于回归样条或 P 样条，提供总共六种方法以在两种模拟方案中进行比较。最后，最具竞争力的方法应用于基于移植物抗宿主病的真实数据集，这是同种异体造血干细胞移植中最常见的并发症之一 (30% -50%)。