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首页> 外文期刊>Annals of the Institute of Statistical Mathematics >Variable selection for functional linear models with strong heredity constraint
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Variable selection for functional linear models with strong heredity constraint

机译：具有强遗传约束的功能线性模型的变量选择

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摘要

In this paper, we consider the variable selection problem in functional linear regression with interactions. Our goal is to identify relevant main effects and corresponding interactions associated with the response variable. Heredity is a natural assumption in many statistical models involving two-way or higher-order interactions. Inspired by this, we propose an adaptive group Lasso method for the multiple functional linear model that adaptively selects important single functional predictors and pairwise interactions while obeying the strong heredity constraint. The proposed method is based on the functional principal components analysis with two adaptive group penalties, one for main effects and one for interaction effects. With appropriate selection of the tuning parameters, the rates of convergence of the proposed estimators and the consistency of the variable selection procedure are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.
机译：在本文中，我们考虑了具有交互作用的函数线性回归中的变量选择问题。我们的目标是确定与响应变量相关的相关主效应和相应的交互作用。在许多涉及双向或高阶相互作用的统计模型中，遗传是一个自然的假设。受此启发，我们提出了一种多功能线性模型的自适应群套索方法，该方法在服从强遗传约束的同时自适应选择重要的单功能预测因子和成对相互作用。该方法基于功能主成分分析，具有两个自适应组惩罚，一个用于主效应，一个用于交互作用。通过适当选择调谐参数，可以确定所提出的估计器的收敛率和变量选择程序的一致性。仿真研究验证了所提程序的性能，并分析了实际算例，说明了该方法的实际应用。

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