Censored Regression with Serially Correlated Errors: a Bayesian approach

TL;DR

This paper introduces a Bayesian Gibbs sampling method for censored linear regression models with autocorrelated errors, effectively handling high censorship and autocorrelation in environmental and social data.

Contribution

It develops a novel Bayesian approach with data augmentation for censored regression models with AR(p) errors, improving estimation accuracy in complex scenarios.

Findings

High accuracy estimates even with large censorship

Effective handling of autocorrelated errors in censored data

Successful application to real environmental data

Abstract

The problem of estimating censored linear regression models with autocorrelated errors arises in many environmental and social studies. The present work proposes a Bayesian approach to estimate censored regression models with AR(p) errors. The algorithm developed here considers the Gibbs sampler with data augmentation(GDA), in which, at each iteration, both the model parameters and the latent variables are sampled. The data augmentation is achieved from multiple sampling of the latent variables from the corresponding conditional distributions. A suitable variable transformation allows the full likelihood to be obtained. A simulation study indicates that the proposed approach produces estimates with a high accuracy even in scenarios where the proportion of censored observations is large. The method is further illustrated in a real data of cloud ceiling height, including model checking and selection for censored time series data.