The Estimation of Nonparametric Functions in a Hilbert Space
提出一种正交级数估计量来估计非线性回归函数，该函数不预设参数形式，并利用希尔伯特空间方法推导其性质与收敛定理，为确定需估计的傅里叶系数个数提供理论依据。
This paper is concerned with the estimation of a nonlinear regression function which is not assumed to belong to a prespecified parametric family of functions. An orthogonal series estimator is proposed, and Hilbert space methods are used in the derivation of its properties and the proof of several convergence theorems. One of the main objectives of the paper is to provide the theoretical basis for a practical stopping rule which can be used for determining the number of Fourier coefficients to be estimated from a given sample.