Robust and Accurate Inference via a Mixture of Gaussian and Student’s <i>t</i> Errors

A Gaussian measurement error assumption, that is, an assumption that the data are observed up to Gaussian noise, can bias any parameter estimation in the presence of outliers. A heavy tailed error assumption based on Student’s <i>t</i> distribution helps reduce the bias. However, it may be less efficient in estimating parameters if the heavy tailed assumption is uniformly applied to all of the data when most of them are normally observed. We propose a mixture error assumption that selectively converts Gaussian errors into Student’s <i>t</i> errors according to latent outlier indicators, leveraging the best of the Gaussian and Student’s <i>t</i> errors; a parameter estimation can be not only robust but also accurate. Using simulated hospital profiling data and astronomical time series of brightness data, we demonstrate the potential for the proposed mixture error assumption to estimate parameters accurately in the presence of outliers. Supplemental materials for this article are available online.