Robust Estimation Using Student's t Distribution

Robust estimators are useful when observations contain gross errors or are sampled from a heavy-tailed distribution. Student's t distributions with small degrees of freedom have heavy tails. Therefore, maximum likelihood estimation using these distributions provides simultaneous robust estimates of location and scale. In addition, the likelihood values can be used to choose among the available t distributions, making it unnecessary to make a subjective choice of an estimator. Monte Carlo results show these estimators to be as efficient as the bi-weight estimators of location and scale.