异常点检测后的偏最小二乘回归模型

偏最小二乘回归是通过一组自变量来预测一个或一组因变量的统计方法。但在很多情况下用于建模的样本点由于种种原因会出现一些异常情况,这些异常点和其他样本点之间都存在着很大的偏差。异常点的存在对所建立的模型和真实模型就有很大的偏差。基于这一问题本文通过构造统计量对所给的样本点进行选择,剔除对模型的构造有很大影响力的样本异常点,从而获得一个相对合理的样本空间。在相对合理的样本空间中采用偏最小二乘回归建立模型。运用MATLAB编程,通过一个实例说明在对于异常点剔除后的样本空间中建立模型的精确程度有了很大的提高。

The model of partial least squares regression after outlier detection

Partial least squares regression is a statistical method which is based on a set of dependent variables to predict the independent variables. However, because of various reasons, the sample points have some outliers that have great deviation in many cases. The model based on the samples that have outliers has a great deviation to the actual situation. Based on this problem, this article selects the sample points by constructing statistics. First, it removes the outliers to have a relatively reasonable sample space. Then it builds a model by partial least squares regression on the obtained sample space. In this paper, we made a model to illustrate that after striking the outliers in the sample space the precision of the established model has greatly improved.