基于自适应Metropolis算法的 α 稳定分布参数估计

基于马尔可夫链蒙特卡罗(Markov chain Monte Carlo, MCMC)方法的α稳定分布参数估计具有良好的性能，但不合适的提议函数常导致算法不收敛或混合性能不好。针对提议函数难以选择的问题，提出了一种基于自适应Metropolis算法的非对称α稳定分布参数估计新方法。该方法利用Markov链的历史信息自动调整提议函数的协方差矩阵，使其不断地逼近目标分布，从而获得更好的估计结果。理论分析和仿真结果表明,此方法不仅能准确地估计出α稳定分布的4个参数，而且具有良好的鲁棒性和灵活性。

Parameter estimation of α-stable distributions based on adaptive Metropolis algorithm

Markov chain Monte Carlo(MCMC) methods for the parameter estimation of α-stable distributions have good performance,but an improper choice of proposal distributions can often lead to unexpected results.Aiming at the difficulties to choose an effective proposal distribution,a novel method based on adaptive Metropolis(AM) algorithm is proposed for non-symmetric α-stable distributions.The method uses the full history(cumulated so far) of the chain to tune the covariance of the proposal distribution suitably.This adaptation strategy can approach an approximation of the target distribution,which increases the efficiency of the simulation.Theoretic analysis and simulation results show that this method can not only estimate the four parameters of α-stable distributions,but also perform very accurately and robustly.