极大似然估计算法研究  

An advanced algorithm for equations of maximum likelihood estimation

作　　者：戴家佳[1,2] 杨爱军[2] 杨振海[2] 

机构地区：[1]贵州大学理学院,贵州贵阳550025 [2]北京工业大学应用数理学院,北京100124

出　　处：《高校应用数学学报（A辑）》2009年第3期275-280,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：北京市属市管高等学校人才强教计划(05006011200702);黔科合J字[2008]2048号

摘　　要：将解一元方程的二分法推广至求解多元非线性方程组.以第k个变元x_k为参数,则k元方程组就可以看作曲线s(前k-1个方程)和k-1维曲面C(第k个方程),于是k元方程组的解就可以看作寻找曲线s和曲面C的交点.对参数x_k作二分法,重复迭代,直到找到满足误差要求的方程组的解.最后给出了用多元二分法的算法求解极大似然估计的数值解.In this paper, the bisection of nonlinear equation is extended to solve nonlinear system of equations involving k nonlinear equations in k variables. The kth variable is considered to be a parameter, therefore the root of the system of multivariate nonlinear equations is the point of intersection between a curve（first k - 1 equations） and a surface（the kth equation） in R^k. The kth variable is divided using the bisection, then the iteration method is used to find the root of system of equations.Finally, the numerical maximum likelihood estimation is obtained by the proposed method.

关 键 词：极大似然估计 二分法 参数估计 

分 类 号：O212.1[理学—概率论与数理统计]