基于二项稀疏算子的二维整数值自回归过程的建模与经验似然推断

发布时间：2018-05-25 20:57

本文选题：二维整数值时间序列 + 经验似然　；参考：《吉林大学》2016年博士论文

【摘要】：本文主要研究了基于二项稀疏算子的二维整数值自回归过程的建模与经验似然推断问题.首先,针对含有二项稀疏算子的二维一阶整数值自回归(BINAR(1))过程,利用经验似然方法建立参数的经验似然比统计量,给出其极限分布以此构造参数的置信域,提出参数的假设检验问题.其次,利用极大经验似然估计方法给出参数的点估计量,并讨论了该估计量的极限性质.最后,我们建立了以二维零截断泊松分布为边际分布,基于二项稀疏算子的二维一阶混合整数值白回归(ZTBPINAR(1))过程,研究了该过程的概率统计性质,并证明了该过程的严平稳性及遍历性,同时利用多种估计方法讨论了参数估计问题,证明估计量的极限性质,同时基于某实例与其他同类模型进行比较,得出评价结果.
[Abstract]:In this paper, the modeling and empirical likelihood inference of 2-D integral numerical autoregressive processes based on binomial sparse operators are studied. Firstly, for the 2-D one-order integral numerical autoregressive (BINAR1) process with binomial sparse operators, the empirical likelihood ratio statistics of parameters are established by means of empirical likelihood method, and their limit distributions are given to construct the confidence regions of the parameters. The hypothesis test problem of parameters is proposed. Secondly, the point estimator of the parameter is given by using the maximum empirical likelihood estimation method, and the limit property of the estimator is discussed. Finally, we establish a two-dimensional one-order mixed integer white regression process based on binomial sparse operator with 2-D zero-truncated Poisson distribution as the marginal distribution, and study the probability and statistical properties of the process. The strict stationarity and ergodicity of the process are proved. At the same time, the parameter estimation problem is discussed by using a variety of estimation methods, and the limit property of the estimator is proved. At the same time, the evaluation results are obtained by comparison with other similar models based on an example.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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