Selection of Fitting Functions in High Dimension

An and Owen（2001）提出拟回归方法逼近高维空间的未知函数。这种方法具有非常高的计算效率，特别是针对样本容量很大的问题。本文基于拟回归构造了很多未知函数的拟合函数，从中选择最好的拟合函数作为这个未知函数的逼近。我们演示了所得到的拟合函数比原拟回归方法具有更小的残差平方和。同时，给出了一个数值模拟的例子。

關鍵字

计算机试验；最小二乘估计；拟回归

並列摘要

An and Owen (2001) introduced quasi-regression for approximating an unknown function in high dimensions. This approach has very high computational efficiency, particularly when samples size is very large. In this paper, we construct many fitting functions of an unknown function based on quasi-regression, and take the best one from them as the resulting approximation of the unknown function. We show the fitting function obtained has less residual sum of squares than original quasi -regression. An example is given for illustrations at the end of this paper.

並列關鍵字

Computer experiment ； least square estimate ； quasi-regression

參考文獻

An, J.,Owen, A. B.(2001).Quas-regression.Journal of Complexity.17,588-607.

Google Scholar

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