Robust estimation with the weighted trimmed likelihood estimator

We consider the problem related to the estimation of parametric models in the presence of outliers. The maximum likelihood estimator is often used to find parameter values. However, it is highly sensitive to abnormal points. In this regard, the weighted trimmed likelihood estimator (WTLE) has been introduced as a robust alternative. We present a new scheme for automatically computing the trimming parameter and weights of the WTLE. The method is illustrated by applying it to the standard GARCH model. We compare the approach with other recently introduced robust GARCH estimators through an extensive simulation study.