Censored regression models with autoregressive errors: A likelihood‐based perspective

In many studies that involve time series variables limited or censored data are naturally collected. Practitioners commonly disregard censored data cases or replace these observations with some function of the limit of detection, which often results in biased estimates. In this article we propose an analytically tractable and efficient stochastic approximation of the EM (SAEM) algorithm to obtain the maximum likelihood estimates of the parameters of censored regression models with autoregressive errors of order, say, p . This approach permits easy and fast estimation of the parameters of autoregressive models when censoring is present and as a byproduct, enables predictions of unobservable values of the response variable. We use simulations to investigate the asymptotic properties of the SAEM estimates and prediction accuracy. Finally the method is illustrated using two time series data sets, where the measurements are subject to the detection limit of the recording devices. The proposed algorithm and methods are implemented in the new R package “ARCensReg.” The Canadian Journal of Statistics 45: 375–392; 2017 © 2017 Statistical Society of Canada