保序调整对线性回归影响的试验分析

采用数学试验方法模拟随机变量,考察满足序关系的变量关于自变量的线性回归,研究并对比在这种情况下直接应用最小二乘线性回归与先对观察到的因变量使用PAVA算法进行保序调整再应用最小二乘线性回归的优劣。结果表明实际应用中,首先进行PAVA算法作调整并不一定是好的,尤其当数据量比较大的时候,其并不能提高拟合效果反而增加工作量。当因变量满足序关系时,直接做最小二乘回归,无需对因变量使用PAVA算法作调整。

Experimental analysis of the influences of order- preserving adjustment on linear regression

The method of mathematical experiment is adopted to simulate the linear regression of variables which meet orderpreserving relation on the independent variable.Both the advantages and disadvantages of two arithmetic are studied,one using least-squares linear regression directly and the other using least-squares linear regression after dependent variable adjustment by PAVA algorithm.The results show that PAVA algorithm is not always the best choice and may increase the work load rather than improve the simulating results in practical use,especially with data in large quantities.It is better to use the algorithm of least-squares linear regression directly with no dependent variable adjustment by PAVA algorithm when the dependent variable meets orderpreserving relation.