Adaptive Robust Estimation by Simulation

William C. Wojciechowski
Rice University


Robust procedures are designed to have stability in the
presence of anomalous data. However, in order to achieve
robustness, some amount of efficiency must be forfeited.
Unfortunately, this tradeoff occurs even when the true
distribution agrees with the model. There is usually no
notion of, or attempt to determine, the optimal balance
between robustness and efficiency. We propose a new
procedure that adapts to the data and automatically selects
the amount of efficiency to sacrifice for robustness.
This procedure couples simulation and data augmentation
to achieve robustness by weighting the observations in
the likelihood function.
We present the new method and examples of its use.

Joint work with David W. Scott and Dennis D. Cox