To deal with the region selection problem in functional linear models, a functional information criterion is suggested to identify the null region where the functional predictor has no contribution to the response. It is shown that the null region identified by our proposal is asymptotically consistent under some mild conditions. In addition, we obtain the convergence rate of the length of the null region estimate, which has not been considered before. The procedure is easily implementable in practice. The finite sample performance is illustrated in applications to simulated and real data.

中文翻译：

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函数线性模型中区域选择的函数信息准则

为了处理函数线性模型中的区域选择问题，建议使用函数信息标准来识别函数预测器对响应没有贡献的无效区域。结果表明，我们的提议确定的空区域在一些温和条件下是渐近一致的。此外，我们获得了之前没有考虑过的空区域估计长度的收敛速度。该程序在实践中很容易实施。在模拟和真实数据的应用中说明了有限样本的性能。