Censored autoregressive regression models with Student-$t$ innovations

Abstract

This paper proposes an algorithm to estimate the parameters of a censored linear regression model when the regression errors are autocorrelated, and the innovations follow a Student-t distribution. The Student-t distribution is widely used in statistical modeling of datasets involving errors with outliers and a more substantial possibility of extreme values. The maximum likelihood (ML) estimates are obtained throughout the SAEM algorithm [1]. This algorithm is a stochastic approximation of the EM algorithm, and it is a tool for models in which the E-step does not have an analytic form. There are also provided expressions to compute the observed Fisher information matrix [2]. The proposed model is illustrated by the analysis of a real dataset that has left-censored and missing observations. We also conducted two simulations studies to examine the asymptotic properties of the estimates and the robustness of the model.