People employ the function-on-function regression to model the relationship between two stochastic processes. Fitting this model, widely used strategies include functional partial least squares algorithms which typically require iterative eigen-decomposition. Here we introduce a route of functional partial least squares based upon Krylov subspace. Our route can be expressed in two forms equivalent to each other in exact arithmetic: One is non-iterative with explicit expressions of the estimator and prediction, facilitating the theoretical derivation and potential extensions; the other one stabilizes numerical outputs. The consistency of estimation and prediction is established under regularity conditions. It is highlighted that our proposal is competitive in terms of both estimation and prediction accuracy but consumes much less execution time.

人们使用功能对功能的回归模型来模拟两个随机过程之间的关系。拟合该模型，广泛使用的策略包括通常需要迭代特征分解的函数偏最小二乘算法。在这里，我们介绍基于Krylov子空间的泛函偏最小二乘路由。我们的路线可以用两种在精确算术上彼此等效的形式表示：一种是非迭代的，其中包含估算器和预测的显式表达式，有利于理论推导和潜在扩展。另一个稳定数值输出。估计和预测的一致性是在规则性条件下建立的。需要强调的是，我们的建议在估计和预测准确性方面都具有竞争力，但消耗的执行时间却少得多。