Censored autoregressive regression models with Student-$t$ innovations

TL;DR

This paper introduces a robust censored autoregressive regression model with Student-$t$ errors, estimated via a stochastic EM algorithm, suitable for datasets with outliers, censoring, and autocorrelation.

Contribution

It develops a novel estimation algorithm for censored autoregressive models with Student-$t$ errors, handling autocorrelation and censored data effectively.

Findings

The proposed method successfully estimates parameters in censored, autocorrelated data.

Simulation studies confirm the robustness and asymptotic properties of the estimates.

Application to real data demonstrates practical utility.

Abstract

The Student-$t$ distribution is widely used in statistical modeling of datasets involving outliers since its longer-than-normal tails provide a robust approach to hand such data. Furthermore, data collected over time may contain censored or missing observations, making it impossible to use standard statistical procedures. 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. To fit the proposed model, maximum likelihood estimates are obtained throughout the SAEM algorithm, which is a stochastic approximation of the EM algorithm useful for models in which the E-step does not have an analytic form. The methods are 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.