Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1  

作　　者：Louis G. Doray Andrew Luong El-Halla Najem Louis G. Doray;Andrew Luong;El-Halla Najem(Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada;école d’Actuariat, Université Laval, Québec, Canada)

机构地区：[1]Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Canada [2]école d’Actuariat, Université Laval, Québec, Canada

出　　处：《Open Journal of Statistics》2016年第4期637-650,共14页统计学期刊（英文）

摘　　要：Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

关 键 词：Discrete Time Series Autoregressive Process Moment Estimator QUASI-LIKELIHOOD EFFICIENCY Generalized Poisson Quasi Binomial Distribution 

分 类 号：O17[理学—数学]