Quasi-Likelihood Estimation of a Censored Autoregressive Model With Exogenous Variables

• 成果类型: Article
• 署名作者: Wang, Chao; Chan, Kung-Sik
• 署名单位: University of Iowa
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2017.1307115
• 发表日期: 2018
• 页码: 1135-1145
• 关键词: regression-analysis; linear-regression

摘要

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.