Abstract: Objective Find out the relationship between the precisionsof 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.

Key words: Multinomial Distribution, Confidence Region, Precisionof Estimation