大样本条件下多项分布未知参数置信域的研究

A Study to the Confidence Region of Multinomial Distribution on the Condition of Large Sample Size

目的找出多项分布某个或某些参数的估计精度与其他参数的关系。方法在大样本条件下由整体参数的置信域出发推导某个或某些参数的置信域。结果给出了多项分布某个或某些参数的置信域与其他参数之间的量化关系。结论若对多项分布的未知参数进行最大似然估计,若某个或某些参数的估计与其真值越接近,则对其他参数估计的精度就会降低。

Objective Find out the relationship between the precisions of estimation of a parameter or some parameters and other parameters. Methods Infer a parameter＇s or some parameters＇ confidence region from the confidence region of entire parameters on the basis of large sample size. Results Give out the quantitative relationship between a parameter＇s or some parameters＇confidence region and other parameters. Conclusion If the unknown parameters of Multinomial Distribution are estimated by MLE and the estimation of a parameter or some parameters is closer to the truth - value, the precisions of estimation of other parameters will be lower.