An Analysis of a Heuristic Procedure to Evaluate Tail (in)dependence

Table 3

Absolute bias and root mean squared error (rmse) of estimator 𝜂.

	𝑛=250	𝑛=1000	𝑛=2500
	bias (rmse)	bias (rmse)	bias (rmse)
𝑏=0.0025
Normal (𝜌=0.5)	0.0901 (0.1513)	0.0579 (0.1109)	0.0457 (0.0887)
Normal (𝜌=0.85)	0.1581 (0.1905)	0.0915 (0.1244)	0.0691 (0.0980)
Student t (𝜌=0.5)	0.1671 (0.2045)	0.0892 (0.1286)	0.0675 (0.1035)
Studentt (𝜌=0)	0.2575 (0.3038)	0.1523 (0.2001)	0.1044 (0.1511)
Logistic	0.1776 (0.2132)	0.0991 (0.1383)	0.0729 (0.1062)
A. Logistic	0.1817 (0.2174)	0.1096 (0.1467)	0.0763 (0.1092)
Morgenstern	0.0217 (0.0950)	0.0166 (0.0674)	0.0159 (0.0520)
𝑏=0.005
Normal (𝜌=0.5)	0.0852 (0.1456)	0.0582 (0.1071)	0.0456 (0.0835)
Normal (𝜌=0.85)	0.1454 (0.1808)	0.0885 (0.1203)	0.0691 (0.0944)
Student t (𝜌=0.5)	0.1552 (0.1923)	0.0876 (0.1256)	0.0661 (0.1003)
Student t (𝜌=0)	0.2614 (0.3066)	0.1570 (0.2010)	0.1080 (0.1504)
Logistic	0.1700 (0.2062)	0.0981 (0.1358)	0.0721 (0.1027)
A. Logistic	0.1722 (0.2038)	0.1070 (0.1423)	0.0755 (0.1062)
Morgenstern	0.0219 (0.0908)	0.0172 (0.0660)	0.0168 (0.0506)
𝑏=0.01
Normal (𝜌=0.5)	0.0847 (0.1425)	0.0584 (0.1011)	0.0462 (0.0794)
Normal (𝜌=0.85)	0.1403 (0.1751)	0.0868 (0.1132)	0.0680 (0.0890)
Studentt (𝜌=0.5)	0.1541 (0.1903)	0.0866 (0.1205)	0.0631 (0.0940)
Studentt (𝜌=0)	0.2658 (0.3085)	0.1616 (0.2006)	0.1159 (0.1496)
Logistic	0.1677 (0.2023)	0.0977 (0.1314)	0.0720 (0.0985)
A. Logistic	0.1692 (0.2038)	0.1074 (0.1397)	0.0742 (0.1018)
Morgenstern	0.0231 (0.0887)	0.0187 (0.0630)	0.0181 (0.0484)
𝑏=0.015
Normal (𝜌=0.5)	0.0843 (0.1389)	0.0587 (0.0987)	0.0465 (0.0751)
Normal (𝜌=0.85)	0.1369 (0.1705)	0.0870 (0.1101)	0.0678 (0.0849)
Student t (𝜌=0.5)	0.1529 (0.1869)	0.0867 (0.1180)	0.0592 (0.0874)
Studentt (𝜌=0)	0.2704 (0.3110)	0.1693 (0.2027)	0.1254 (0.1522)
Logistic	0.1667 (0.2000)	0.0980 (0.1284)	0.0711 (0.0943)
A. Logistic	0.1671 (0.1998)	0.1081 (0.1382)	0.0718 (0.0963)
Morgenstern	0.0231 (0.0861)	0.0203 (0.0609)	0.0197 (0.0469)