基于SA-MCMC算法的非线性测量误差模型数据删除影响

Deletion influence of nonlinear measurement error models based on SA-MCMC algorithms

为了研究非线性测量误差模型强影响点的识别问题,首先将非线性测量误差模型中存在误差的不可观测的数据当作缺失数据,利用SA-MCMC算法求得模型参数的最大似然估计,然后用Q函数代替可观测数据的对数似然函数进行影响分析,得到了建立在Q函数基础上的广义Cook距离及其一步近似,最后通过算例说明了诊断统计量的有效性.

The deletion measures for nonlinear measurement error models were studied. The unobservable measurement errors were treated as the missing data. The maximum likelihood estimates were obtained using the stochastic approximation algorithms with the Markov Chain Monte Carlo （SA-MCMC） method. The logarithmic likelihood function of the observable data was replaced by the Q function. The Cook＇s distance and its one-step approximation were derived based on the Q function. The effectiveness of the diagnostic measures was validated with a real example.