标题： 非参数局部多项式回归，用于函数型协变量 显示英文标题

标题： Nonparametric local polynomial regression for functional covariates

摘要： 我们研究了具有函数型协变量的非参数回归问题，即它们是无穷维Hilbert空间中的元素。 构造了一个局部多项式估计量，其中需要选择一组正交基和多个调节参数。 我们给出了估计误差的一般渐近上界，并证明了在适当的调节参数和回归函数的超光滑性条件下，该方法能够达到多项式收敛速度。 通常情况下，在没有额外强结构约束（例如回归函数的线性）的情况下，非参数函数型回归被认为无法达到这种多项式收敛速度。 显示英文摘要

摘要： We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters remain to be selected. We provide a general asymptotic upper bound on the estimation error and show that this procedure achieves polynomial convergence rates under appropriate tuning and supersmoothness of the regression function. Such polynomial convergence rates have usually been considered to be non-attainable in nonparametric functional regression without any additional strong structural constraints such as linearity of the regression function.