有关顺序统计量的极大似然估计

讨论了一类参数空间受样本限制的极大似然估计问题.分析了随机变量分布的非零区域与似然函数定义域的对应关系,提出如果分布的非零区域受参数限制,则无论似然方程是否可解,参数的极大似然估计必然与样本顺序统计量X_((n))或X_((1))有关,并具体分析了似然估计一定等于、一定不等于和可能等于顺序统计量X_((n))(X_((1)))的三种情形,并给出了相应的判别条件.最后分析得出在第三种判别条件之下,似然估计是否取值于x_((n))(x_((1)))视具体的样本观测值决定.

The Maximum Likelihood Estimation with the Order Statistics

In this paper,a class of parameter space restricted by the sample maximum likelihood estimation problem is discussed.The corresponding relationship is considered between non-zero region in distribution of a random variable and the domain of likelihood function.The paper proposed that no matter the likelihood equation is solvable or not,if the distribution of non-zero region affected by parameter restrictions,the maximum likelihood estimation of parameters related to the order statistics X_((n)) or X_((1)) inevitably.This maximum likelihood estimation has three cases:equal,not equal or possible equal to the order statistics,and gives the corresponding Criterion.Finally,it is obtained that under the possible equal case,the likelihood estimation is X_((n)) or X_((1)) depends on the sample observations.