线性回归模型的最小二乘法基本假设在Z-I关系拟合中的应用

Application of elementary assumptions of least square method in linear regress model to Z-I relation

由于Z-I关系的非线性,线性回归模型中常规最小二乘法的一些基本假设在拟合过程中无法满足。研究表明使用不同的计算方法,同样的数据可能得到差异明显的A、b值。本文从常规最小二乘法基本假设入手,通过2006年大连地区两次降水过程的回波和雨量资料,对不同Z-I回归模型中关于误差项的物理意义、期望和方差进行比较,提出在Z-I拟合中采用加权最小二乘法。

Due to the nonlinearity in Z-I relation, some elementary assumptions of ordinary least squares method in linear regress model are not satisfied in the fitting process. It is showed in some researches that different estimate methods may get different A and b values with same data. With the radar echo and precipitation data of two precipitation process in Dalian in 2006, the physics meaning, expectation and variance of errors in different models are compared in the paper, and weighted least squares method is proposed to fit Z-I relation.