College of Liberal Arts & Sciences
Chao Wang - Colloquium Speaker
Maximum likelihood estimation of a censored autoregres-sive model with exogenous variables (CARX) requires computing the conditional likelihood of blocks of data of variable dimensions. As the random block dimension gen-erally 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 computa-tionally 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. An accompanying R package will also introduced.