基于假设函数空间上样本误差的估计

Estimation of Sample Error Based on Hypothesis Space

在传统回归分析中,基于已知样本寻找最优函数一般在某个已知函数空间,如多项式空间,对数以及指数空间等,对于样本个数一定的情况下,样本误差会随着函数空间的增大而增大.在本文中,作者用概率测度、覆盖原理在有界函数空间中给出一个样本误差估计的方法.

In traditional regress analysis, a good regression function is found in some function space based on known samples, such as polynomial function space, logarithm space and exponent space, When the sample number is certain the sample error will be big with the widening of function apace. In this paper, a method of sample error estimation is presented by probability measure and covering theory in a bouded function space.