Identification and Robustness with Contaminated and Corrupted Data

Robust estimation aims at developing point estimators that are not highly sensitive to errors in data. However, the population parameters of interest are not identified under the assumptions of robust estimation, so the rationale for point estimation is not apparent. This paper shows that, under error models used in robust estimation, unidentified population parameters can often be bounded. The bounds provide information that is not available in robust estimation. For example, it is possible to bound the population mean under contaminated sampling. It is argued that estimating the bounds is more natural than attempting point estimation of unidentified parameters.