Lee Sangyeol, Kim Dongwon
Department of Statistics, Seoul National University, Seoul 08826, Korea.
Entropy (Basel). 2020 Nov 16;22(11):1304. doi: 10.3390/e22111304.
In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.
在本研究中，我们考虑一种在线监测程序，用于检测整数值广义自回归条件异方差（INGARCH）模型的参数变化，该模型中当前观测值相对于过去信息的条件密度服从单参数指数族分布。为此，我们使用从目标函数推导的得分函数的累积和（CUSUM），这些目标函数是为包括最大似然估计器（MLE）的最小功率散度估计器（MDPDE）构建的，以减少异常值的影响。众所周知，与MLE相比，MDPDE对异常值具有鲁棒性，且效率损失很小。所提出的监测程序恰当地继承了这种鲁棒性。进行了模拟研究和实际数据分析以证实我们方法的有效性。
