In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary goal is prediction, we show that the gain by embedding the problem into a scalar-on-function regression is limited. Instead we impose a factor model on the predictors and suggest regressing the response on an appropriate number of factor scores. This approach is shown to be consistent under mild technical assumptions, numerically efficient and gives good practical performance in both simulations as well as real data settings.

翻译：实际上,功能数据是在一组离散的观察点上抽样的,往往容易受到噪音的影响。我们在本文件中将这些数据用作回归问题的解释变量。如果主要目标是预测,我们则表明,将问题嵌入一个卡尔-功能回归的收益是有限的。我们反而对预测器强加一个要素模型,并建议在适当数量的因数分数上退退退反应。在温和的技术假设下,这种方法是一致的,具有数字效率,在模拟和真实数据设置中都具有良好的实际性能。