基于信息扩散原理的估计理论、方法及其抗差性

The Theory, Method and Robustness of the Parameter Estimation Based on the Principle of Information Spread

介绍了适合小样本情况下估计概率密度函数的信息扩散理论，导出了参数估计的信息扩散估计法——ＩＳＥ（ｉｎｆｏｒｍ ａｔｉｏｎ ｓｐｒｅａｄ ｅｓｔｉｍ ａｔｉｏｎ）。理论和实践表明，ＩＳＥ法可以在小样本情况下估计母体的概率密度函数。该方法不仅具有良好的抗差性，而且具有方法简便、便于应用等优点。

It is supposed that the observations obey a certain distribution in all the methods of parameter estimation to this day. But in the practical surveying, due to the different observation conditions, the observations obtained under different observation conditions may obey different distributions. So the supposition is not conform to reality. The idea that conform to reality should be that the distribution of the observation is estimated based on the observations before estimated parameter. According to the idea, this paper introduces the theory of information spread at first. Then the method of information spread estimation (ISE) has been presented. The theory and calcultion indicate that ISE not only has fine robustness, but also it is very simple and convenient for application.