Additive functional model is one popular semiparametric approach for regression with a functional predictor. Optimal prediction error rate has been demonstrated in the framework of reproducing kernel Hilbert spaces (RKHS), which only depends on the property of the RKHS but not on the smoothness of the function. We extend this previous theoretical result by establishing faster convergence rates under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result shows that with a smoother function the convergence rate of the estimator is faster.

中文翻译：

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在平滑条件下再现核 Hilbert 空间的加性函数回归

加性函数模型是一种流行的半参数回归方法，具有函数预测器。最优预测错误率已经在再现核希尔伯特空间（RKHS）的框架中得到证明，该框架仅取决于 RKHS 的性质，而不取决于函数的平滑度。我们通过在更强的条件下建立更快的收敛速度来扩展先前的理论结果，当去除更强的条件时，收敛速度会降低到现有结果。特别是，我们的结果表明，使用更平滑的函数，估计器的收敛速度更快。