Table 2.

 MSE $(\times {10}^3)$ (mean squared [estimate minus true α]) for tail-index estimators $B_1,B_2,B_3$, HI.N, HI.M, HI.Opt, and MHB3 with sample size $n={10}^4$ from $F(1,\alpha )$

α	B1	B2	B3	HI.N	HI.M	HI.Opt	MHB3
0.1	0.14	0.15	0.11	2.61	20.06	0.02	0.10
0.2	0.53	0.58	0.35	4.73	9.13	0.09	0.31
0.3	1.13	1.23	0.71	7.33	6.31	0.19	0.57
0.4	1.86	1.96	1.16	9.15	6.39	0.34	0.85
0.5	2.60	2.66	1.76	9.12	6.76	0.54	1.15
0.6	3.47	3.20	2.32	7.93	6.13	0.84	1.53
0.7	4.15	3.38	2.60	6.46	5.30	1.52	1.94
0.8	4.32	3.05	2.28	6.97	6.67	4.35	2.13
0.9	3.59	2.10	1.33	57.51	58.26	26.36	1.33