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Often it is not easy to choose between estimators, based on the estimated MSEand bias using simulation studies. Normality in small samples and a variance ofthe estimator, which is correct and easy to calculate using a single sample,give the added advantage that hypotheses concerning the parameter can be testedin new samples. A procedure to check normality is proposed where previouslypublished MSE and bias are used to perform a test for normality. A confidenceinterval for the index of the S&P500 index is found by applying the results toestimators of the generalized Pareto distribution.

Testing approximate normality of an estimator using the estimated MSE  and bias with an application to the shape parameter of the generalized Pareto  distribution