数论网格法在极大似然估计中的应用

Application of Number Theoretic Methods in Maximum Likelihood Estimation

复杂似然函数的多峰性使得极大似然估计的求解存在很大困难。针对这一问题,提出了求解极大似然估计问题的数论网格法。讨论了数论网格法的特点,理论分析了其算法精度,给出了基于数论网格的序贯优化算法的计算步骤,研究了初始搜索区域和算法初始参数的确定方法。最后,以两参数威布尔分布参数极大似然估计为例,给出了极大似然估计的计算过程,比较了序贯优化算法和对分法的估计结果,说明了序贯优化算法的有效性和计算效率。

The multi-peak of complex likelihood function causes the difficulty to gain maximum likelihood estimators, The number theory method was applied to get maximum likelihood estimators, The characteristic of number theory method was discussed. The arithmetic precision was theoretically analyzed, Based on the number theory net, the computable steps of sequential number-theoretic method for optimization （SNTO） were proposed. Thus, the method was researched to decide initial searched domain and initial parameters, Lastly, an example was shown to illustrate the maximum likelihood estimators （MLE） for weibull distribution, and the computation of MLEs was proposed, The results were compared from SNTO and bisection method, and the validity and efficiency of SNTO were shown.