Quasi-Likelihood Estimation of a Censored Autoregressive Model With Exogenous Variables
针对带外生变量的删失自回归模型，提出一种基于完全-不完全数据框架的拟似然估计方法，解决了最大似然估计在删失率增加时计算困难的问题，并证明了估计量的一致性和渐近正态性。
Maximum likelihood estimation of a censored autoregressive model with exogenous variables (CARX) requires computing the conditional likelihood of blocks of data of variable dimensions. As the random block dimension generally increases with the censoring rate, maximum likelihood estimation becomes quickly numerically intractable with increasing censoring. We introduce a new estimation approach using the complete-incomplete data framework with the complete data comprising the observations were there no censoring. We introduce a system of unbiased estimating equations motivated by the complete-data score vector, for estimating a CARX model. The proposed quasi-likelihood method reduces to maximum likelihood estimation when there is no censoring, and it is computationally efficient. We derive the consistency and asymptotic normality of the quasi-likelihood estimator, under mild regularity conditions. We illustrate the efficacy of the proposed method by simulations and a real application on phosphorus concentration in river water.