IDENTIFICATION AND ROBUSTNESS WITH CONTAMINATED AND CORRUPTED DATA

Robust estimation aims at developing point estimators that are not hig hly sensitive to errors in the data. However, the population parameter s of interest are not identified under the assumptions of robust estim ation, so the rationale for point estimation is not apparent. This pap er shows that under error models used in robust estimation, unidentifi ed population parameters can often be bounded. The bounds provide info rmation that is not available in robust estimation. For example, it is possible to obtain finite bounds on the population mean under contami nated sampling. A method for estimating the bounds is given and illust rated with an application. It is argued that when the data may be cont aminated or corrupted, estimating the bounds is more natural than atte mpting point estimation of unidentified parameters.