广义二项自回归模型的贝叶斯统计推断  

Bayesian statistical inference of generalized binomial autoregressive model

作　　者：邵思雨 龙琪 张洁 SHAO Siyu;LONG Qi;ZHANG Jie(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2023年第4期375-384,共10页Journal of Changchun University of Technology

基　　金：吉林省自然科学基金(YDZJ202301ZYTS384)。

摘　　要：利用贝叶斯方法研究广义二项自回归模型的参数统计问题,给出模型参数的贝叶斯估计表示式。通过数值模拟将贝叶斯估计与条件极大似然估计和条件最小二乘估计进行比较。其中,贝叶斯估计中的多重积分通过样本平均值法进行计算。其次,还考虑了数据污染情况下模型参数估计的相关研究。最后将模型应用于长沙市每周下雨天数数据中,验证了模型和贝叶斯估计方法的优良性质,并为实际问题的分析提供理论支撑。For finite-range integer-valued time series data with dependent structure,we study the parameter estimation of the generalized binomial autoregressive(GBAR(1))model through the Bayes method.The related expressions of the Bayesian estimators are given.In simulation studies,we compare the Bayesian estimation with the conditional maximum likelihood estimation and the conditional least squares estimation.In this place,the multiple integrals in the Bayesian estimation are calculated by the sample mean method.Secondly,the related research on parameter estimation of GBAR(1)model in the case of data contamination is also considered.Finally,the model is applied to the data of weekly rainy days in Changsha,which verifies the excellent properties of the model and the Bayes estimation method and provides theoretical support for the analysis of practical problems.

关 键 词：广义二项自回归过程 似然函数 贝叶斯估计 样本平均值法 

分 类 号：O212[理学—概率论与数理统计]