最小信息变差与估计初探

A Preliminary Exploration of Minimum Variationm of Information and Estimates

试图用信息变差直接分析和处理有关估计的某些方面,说明信息变差是一个好的度量。本文简化信息变差定理的证明,直接证明指数分布簇的最小信息变差意义,并证明速率函数可以用最小信息变差和最大似然估计法进行估计与计算。

The paper set out to analyse and deal with certain aspects of estimates by exploying information variation of which a good measure was illustrated with extensioness, profoundness, simplification and being perceived through the senses. The first part of the paper emphaticably described the general variation of information and demonstrated a theorem of simplifying the variation of information. Then, the meaning of minimum variation of information in exponential families was demonstrated. Finally, it was proved that the rate function can be estimated and calculated by using minimum variation of information and maximnm likelihood estimates.