带有变量中误差非正态模型中的Box-Cox变换

BOX-COX TRANSFORMATION USED IN NON-NORMAL MODEL WITH ERRORS-IN-VARIABLES

摘要:

Box-Cox变换主要用于得到近似正态分布的随机变量。线性模型中的响应(因)变量Y(或经过变换的Y)通常建立在精确测量无误差的独立变量集上。本文研究独立变量中的测量误差(即变量中误差)对Box-Cox变换中参数估计的影响。研究结果表明,忽略变量中的误差将产生变换参数估计的偏离,该结论由分析论证和随机模拟得以支持。

关键词:Box-Cox变换;变量中误差;非正态;极大似然估计;随机模拟

Abstract:

The Box-Cox transform ation is widely used for obtaining an approximate normaly- distributed random variable.In a linear model setting,a responsive dependent variable Y(or transformed Y)is built on a set of independent variables,usually assumed to be measured with no error.This paper investigates the effects of measurement error in independent variables (known as errors-in-variables)on parameter estimate for the transformation.Ignoring such error in independent variables wil cause biased t ransformation parameter estimate ingeneral,a conclusion that is supported by analytical arguments and stochastical simulation.

Key words:Box-Cox transformation;errors-in-variables;non-normal;maximum likelihood estimation;random simulation