Discussions of papers already published: "Robust and efficient estimation of the tail index of a single-parameter pareto distribution," Vytaras Brazauskas and...

North American Actuarial Journal, Jul 2001 by Bilodeau, Martin, Brazauskas, Vytaras, Serfling, Robert

In Brazauskas and Serfling (2000) we treat the related problem of estimation of ot with sigma unknown. Again the GM estimators dominate the conventional ones with respect to ARE and UBP. Furthermore, it can be shown that the ARE and GES values in this case agree exactly with corresponding values for the case of sigmsknown, so that the trade-offs between ARE and GES are identical in the two cases.

REFERENCES

BRAzAusKAs, V., AND RI SERFLING. 2000. "Robust Estimation of Tail Parameters for Two-Parameter Pareto and Exponential Models via Generalized Quartile Statistics," Extremes 3: 231-49.

2001. "Small Sample Performance of Robust Estimators of Tail Parameters for Pareto and Exponential Models,"

Journal of Statistical Computation and Simulation 70(August), in press.

HAMPEL, F. R. 1974. "The Influence Curve and Its Role in Robust Estimation," Journal of American Statistical Association 69: 383-97.

HAMPEL, F. R., E. M. RONCHETTI, P. J. ROUSSEEUW, AND W. A. STAHEL. 1986. Robust Statistics: The Approach Based on Influence Functions. New York: John Wiley and Sons.

KImBER, A. C. 1983a. Trimming in Gamma Samples. Applied Statistics 32: 7-14.

KMEx, A. C. 1983b. "Comparison of Some Robust Estimators of Scale in Gamma Samples with Known Shape," Journal of Statistical Computation and Simulation 18: 273-86.

SERFLING, R. J. 1980. Approximation Theorems of Mathematical Statistics. New York: John Wiley and Sons.

MARTIN BILODEAU*

* Martin Bilodeau, Ph.D., A.S.A., is in the Departement de mathematiques et de statistique and Centre de recherches mathematiques of Universite de Montreal, C.P. 6128, Succursale Centre-ville, Montreal, Canada H3C 317, email: bilodeau@dms.umontreal.ca.