线性回归中不规则数据的处理方法及其应用

目的：考察不规则数据对经典最小二乘回归的影响，提出处理变量中存在不规则数据的稳健统计分析方法．方法：采用实证方式比较稳健估计与一般最小二乘估计的优劣．结果：实例分析表明，稳健回归估计是处理不规则数据的有效方法。结论：不规则数据对最小二乘回归的影响已引起广泛的注意，提出了一些处理应变量中不规则数据的方法，而对自变量中及自变量与应变量中同时存在的不规则数据无有效的处理方法．本应用稳健统计的思想解决了这一问题，该方法也可直接应用于多元线性回归分析中。

Irregular data process in linear regression and its application

AIM: To inspect the influence of irregular data on least square regression. A robust statistical analysis method was presented for the irregular data in variables. METHODS: The discretion between robust estimator and ordinary least square estimator was shown by a case. RESULTS: It was illustrated by this case that the robust regression estimate was effective method for treating irregular data. CONCLUSION: The influence of irregular data on least square regression arouse extensive attention. Some methods are presented to treat the irregular data in dependent variable. But there are no effective methods to treat irregular data in independent variable or independent and dependent variables. The problem may be solved with robust statistical principle. The method can also directly apply to multivariate regression analysis.