相互近邻域的函数型回归估计

摘要

Let H be a separable Hilbert space, (X, Y) be a random pair taking values in H ×. By considering only the first d coefficients of a Fourier series expansion of each iX , we reduce the dimension of space H , and then prove the consistency of mutual nearest neighbor estimation of the regression function. Both the dimension and the number of neighbors are automatically selected from the observation which uses data dependent splitting devices.%令H为可分的希尔伯特空间,(X,Y)是在H上取值的随机对。本文通过对每个Xi进行d 项傅里叶级数展开，从而将无穷维降到有限维，进而证明了MNN 估计的相容性。其中维数和邻域数都是从观察样本中自动选取的。