对数变换的问题及其改进

在用对数变换方法使幂函数或指数函数的曲线拟合线性化时，人们往往忽视这样的问题：（１）哪些模型结构可以采用对数变换，（２）对数变换会会会改变模型残差的一些性质；（３）这种化曲为直的回归方法估计出的原模型中的参数是否具有无偏性和有效性，针对上述问题做了较为深入的探讨，并提出了相应的改进方法。

Problems in the Logarithmic Transformation and Improvements

The following problems that results from logarithmic transformation linearizes power or exponential model are generally ignored:(1) Which model structures are linearized with logarithmic transformation? (2) Could the error properties be changed under the transformation? (3) Would the regression coefficients of estimate with the transformation be unbiased and minimum-error-variance? Such problems and appropriate improvements are discussed in this paper.