论文标题
快速实施部分最小二乘功能在功能上的回归
Fast implementation of partial least squares for function-on-function regression
论文作者
论文摘要
人们采用功能在功能回归中来模拟两条随机曲线之间的关系。拟合此模型，广泛使用的策略包括属于功能部分最小二乘框架的算法（通常需要迭代特征分解）。在这里，我们介绍了基于Krylov子空间的功能部分最小二乘途径。它可以以两种形式表示相等的形式（确切的算术）：一种是非具有明确形式的估计器和预测形式的，促进了理论推导和潜在的扩展（更复杂的模型）；另一个稳定数值输出。估计量和预测的一致性是在规则条件下建立的。我们的建议被突出显示，因为它在计算上涉及的涉及较少。同时，就估计和预测准确性而言，它具有竞争力。
People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically requiring iterative eigen-decomposition). Here we introduce a route of functional partial least squares based upon Krylov subspaces. It can be expressed in two forms equivalent to each other (in exact arithmetic): one is non-iterative with explicit forms of estimators and predictions, facilitating the theoretical derivation and potential extensions (to more complex models); the other one stabilizes numerical outputs. The consistence of estimators and predictions is established under regularity conditions. Our proposal is highlighted as it is less computationally involved. Meanwhile, it is competitive in terms of both estimation and prediction accuracy.
