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

Table 1

Absolute bias and root mean squared error (rmse) of estimator 𝜆^SEC.

	𝑛=250	𝑛=1000	𝑛=2500
	abs. bias (rmse)	abs. bias (rmse)	abs. bias (rmse)
𝑏=0.0025
Normal (𝜌=0.5)	0.1920 (0.2187)	0.1573 (0.1709)	0.1363 (0.1447)
Normal (𝜌=0.85)	0.5347 (0.5444)	0.4860 (0.4915)	0.4572 (0.4610)
Student t (𝜌=0.5)	0.0098 (0.1262)	0.0022 (0.0875)	0.0048 (0.0666)
Student t (𝜌=0)	0.0057 (0.1091)	0.0016 (0.0773)	0.0037 (0.0601)
Logistic	0.4439 (0.4596)	0.0069 (0.0905)	0.0008 (0.0646)
A. Logistic	0.0007 (0.1254)	0.0057 (0.0921)	0.0001 (0.0701)
Morgenstern	0.0542 (0.0770)	0.0302 (0.0421)	0.0213 (0.0287)
𝑏=0.005
Normal (𝜌=0.5)	0.2055 (0.2298)	0.1650 (0.1772)	0.1471 (0.1541)
Normal (𝜌=0.85)	0.5418 (0.5510)	0.4895 (0.4946)	0.4655 (0.4688)
Student t (𝜌=0.5)	0.0057 (0.1203)	0.0015 (0.0837)	0.0027 (0.0616)
Studentt (𝜌=0)	0.0049 (0.1096)	0.0032 (0.0735)	0.0047 (0.0549)
Logistic	0.0067 (0.1153)	0.0076 (0.0878)	0.0010 (0.0596)
A. Logistic	0.0043 (0.1220)	0.0045 (0.0888)	0.0021 (0.0646)
Morgenstern	0.0614 (0.0841)	0.0334 (0.0448)	0.0256 (0.0322)
𝑏=0.01
Normal (𝜌=0.5)	0.2148 (0.2364)	0.1808 (0.1904)	0.1650 (0.1701)
Normal (𝜌=0.85)	0.5461 (0.5552)	0.4997 (0.5038)	0.4828 (0.4852)
Student t (𝜌=0.5)	0.0043 (0.1158)	0.0006 (0.0750)	0.0001 (0.0542)
Student t (𝜌=0)	0.0089 (0.1057)	0.0062 (0.0660)	0.0061 (0.0476)
Logistic	0.0081 (0.1097)	0.0101 (0.0803)	0.0044 (0.0518)
A. Logistic	0.0054 (0.1170)	0.0004 (0.0798)	0.0056 (0.0566)
Morgenstern	0.0683 (0.0898)	0.0414 (0.0513)	0.0338 (0.0391)
𝑏=0.015
Normal (𝜌=0.5)	0.2234 (0.2428)	0.1939 (0.2017)	0.1810 (0.1849)
Normal (𝜌=0.85)	0.5515 (0.5598)	0.5101 (0.5134)	0.4989 (0.5006)
Student t (𝜌=0.5)	0.0031 (0.1117)	0.0023 (0.0682)	0.0018 (0.0480)
Student t (𝜌=0)	0.0118 (0.1019)	0.0089 (0.0608)	0.0078 (0.0426)
Logistic	0.4500 (0.4621)	0.0124 (0.0738)	0.0076 (0.0463)
A. Logistic	0.0072 (0.1121)	0.0034 (0.0730)	0.0088 (0.0510)
Morgenstern	0.0749 (0.0952)	0.0495 (0.0580)	0.0420 (0.0462)