General purpose optimization routines such as nlminb, optim (R) or nlmixed (SAS) are frequently used to estimate model parameters in nonstandard distributions. This paper presents Particle Swarm Optimization (PSO), as an alternative to many of the current algorithms used in statistics. We find that PSO can not only reproduce the same results as the above routines, it can also produce results that are more optimal or when others cannot converge. In the latter case, it can also identify the source of the problem or problems. We highlight advantages of using PSO using four examples, where: (1) some parameters in a generalized distribution are unidentified using PSO when it is not apparent or computationally manifested using routines in R or SAS; (2) PSO can produce estimation results for the log-binomial regressions when current routines may not; (3) PSO provides flexibility in the link function for binomial regression with LASSO penalty, which is unsupported by standard packages like GLM and GENMOD in Stata and SAS, respectively, and (4) PSO provides superior MLE estimates for an EE-IW distribution compared with those from the traditional statistical methods that rely on moments.

翻译：通用优化程序（如R语言中的nlminb、optim或SAS中的nlmixed）常被用于非标准分布中的模型参数估计。本文提出粒子群优化（PSO）作为统计学中多种现有算法的替代方案。研究发现，PSO不仅能复现上述程序的相同结果，还能在后者无法收敛时产生更优结果，或识别问题的根源。我们通过四个案例突出PSO的优势：（1）当广义分布中的某些参数在R或SAS程序中无法明显识别或计算时，PSO可提供解决方案；（2）在当前程序可能失效的情况下，PSO能对对数二项回归进行参数估计；（3）PSO在带有LASSO惩罚的二项回归中实现了链接函数的灵活性，而这在Stata的GLM和SAS的GENMOD等标准包中不受支持；（4）与依赖于矩估计的传统统计方法相比，PSO能为EE-IW分布提供更优的最大似然估计（MLE）结果。