  A Gaussian measurement error assumption, i.e., 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 t
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 t
errors according to latent outlier indicators, leveraging the best of the
Gaussian and Student's t 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.
