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

Table 2

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

	𝑛=250	𝑛=1000	𝑛=2500
	bias (rmse)	bias (rmse)	bias (rmse)
𝑏=0.0025
Normal (𝜌=0.5)	0.1842 (0.2179)	0.1511 (0.1676)	0.1287 (0.1383)
Normal (𝜌=0.85)	0.5257 (0.5363)	0.4863 (0.4919)	0.4617 (0.4655)
Student t (𝜌=0.5)	0.0214 (0.1256)	0.0092 (0.0857)	0.0096 (0.0665)
Student t (𝜌=0)	0.2896 (0.3111)	0.2725 (0.2835)	0.0060 (0.0608)
Logistic	0.0061 (0.1142)	0.0037 (0.0860)	0.0022 (0.0594)
A. Logistic	0.0085 (0.1198)	0.0076 (0.0830)	0.0022 (0.0630)
Morgenstern	0.0240 (0.0634)	0.0126 (0.0325)	0.0091 (0.0215)
𝑏=0.005
Normal (𝜌=0.5)	0.1930 (0.2235)	0.1557 (0.1704)	0.1363 (0.1444)
Normal (𝜌=0.85)	0.5340 (0.5441)	0.4925 (0.4977)	0.4679 (0.4713)
Student t (𝜌=0.5)	0.0225 (0.1231)	0.0095 (0.0829)	0.0091 (0.0630)
Student t (𝜌=0)	0.0259 (0.1152)	0.0127 (0.0758)	0.0065 (0.0560)
Logistic	0.0046 (0.1108)	0.0041 (0.0819)	0.0017 (0.0544)
A. Logistic	0.0071 (0.1160)	0.0076 (0.0795)	0.0020 (0.0587)
Morgenstern	0.0279 (0.0684)	0.0140 (0.0338)	0.0111 (0.0215)
𝑏=0.01
Normal (𝜌=0.5)	0.1996 (0.2278)	0.1694 (0.1767)	0.1499 (0.1559)
Normal (𝜌=0.85)	0.5400 (0.5497)	0.5008 (0.5052)	0.4784 (0.4809)
Student t (𝜌=0.5)	0.0227 (0.1188)	0.0104 (0.0764)	0.0087 (0.0559)
Student t (𝜌=0)	0.0239 (0.1121)	0.0130 (0.0689)	0.0088 (0.0492)
Logistic	0.0043 (0.1079)	0.0023 (0.0753)	0.0014 (0.0487)
A. Logistic	0.0093 (0.1108)	0.0064 (0.0745)	0.0013 (0.0529)
Morgenstern	0.0313 (0.0712)	0.0175 (0.0362)	0.0147 (0.0251)
𝑏=0.015
Normal (𝜌=0.5)	0.2038 (0.2299)	0.1730 (0.1828)	0.1623 (0.1669)
Normal (𝜌=0.85)	0.5453 (0.5543)	0.5067 (0.5104)	0.4904 (0.4923)
Student t (𝜌=0.5)	0.0228 (0.1156)	0.0114 (0.0708)	0.0094 (0.0501)
Student t (𝜌=0)	0.2823 (0.3015)	0.0273 (0.2800)	0.0111 (0.0445)
Logistic	0.0055 (0.1044)	0.0015 (0.0697)	0.0014 (0.0444)
A. Logistic	0.0085 (0.1073)	0.0061 (0.0700)	0.0008 (0.0489)
Morgenstern	0.0346 (0.0733)	0.0210 (0.0380)	0.0183 (0.0270)