曲线回归分析中的Monte-Carlo方法

A Method on the Basis of MonteCarlo Principle for Evaluation of Curve Regression.

目的：曲线回归分析中如何选择曲线类型是一个比较困难的问题，单纯依靠拟合优度指标有时难以反映孰优孰劣，本文利用ＭｏｎｔｅＣａｒｌｏ原理给出一种评价曲线回归效果的方法，以弥补传统的不足。方法：通过模拟试验（ＳＡＳ程序）给出两个主要的评价统计量，即参数的百分偏差和超出方差，并对参数的性态作出检验。文中列举了应用实例。结果：不同数据模型其参数的百分偏差和超出方差可能有较大的差别，一般百分偏差最好小于１％，超出方差不超过１０％。结论：参数估计的性态是评价模型优劣的一个重要方面，在模型拟合优度相差不大的情况下，应尽量选择性态好的模型。

bjective:How to chose the types of curve is a difficult problem in the anlysis of nonlinear regression.Fitness sometimes can not reflect the which is better or worse.This paper use MonteCarol principle to provide a methods to evaluate the regression effect and compensate the disadvantage of traditional methods.Method:We use the simulation(SAS program)to give two main statistic for evaluation.that are percentage bias and over variance,and test the properties of parameters.The applicable examples are listed in thes paper.Results:Maybe there is a obvious difference in percentage bias and over variance among different datamodels.In general,it is better that the percentage bias is lower than 1%,the over variance is not beyond 10%.[WT5”HZ]Conclusion:The properties of estimating parameter is an important aspect in evaluating the goodness of models.We should do our best to chose a model with good properties when the fitness are similar.This is feasible while using this simulation method.