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

Table 4

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

	𝑛=250	𝑛=1000	𝑛=2500
	bias (rmse)	bias (rmse)	bias (rmse)
𝑏=0.0025
Normal (𝜌=0.5)	0.0543 (0.2429)	0.0202 (0.2869)	0.0446 (0.3047)
Normal (𝜌=0.85)	0.1001 (0.2068)	0.1273 (0.2118)	0.1277 (0.2082)
Student t (𝜌=0.5)	0.3361 (0.3582)	0.3191 (0.3273)	0.3005 (0.3046)
Student t (𝜌=0)	0.5158 (0.5353)	0.5552 (0.5649)	0.5394 (0.5443)
Logistic	0.3180 (0.3391)	0.3042 (0.3130)	0.2952 (0.2992)
A. Logistic	0.3235 (0.3416)	0.3107 (0.3183)	0.2934 (0.2975)
Morgenstern	0.5033 (0.1346)	0.3719 (0.1690)	0.3120 (0.2101)
𝑏=0.005
Normal (𝜌=0.5)	0.0254 (0.2648)	0.0333 (0.2984)	0.0539 (0.3125)
Normal (𝜌=0.85)	0.1134 (0.2157)	0.1310 (0.2147)	0.1325 (0.2122)
Student t (𝜌=0.5)	0.3604 (0.3812)	0.3269 (0.3344)	0.3112 (0.3147)
Student t (𝜌=0)	0.5543 (0.5725)	0.5689 (0.5777)	0.5523 (0.5566)
Logistic	0.3345 (0.3530)	0.3122 (0.3203)	0.3078 (0.3112)
A. Logistic	0.3395 (0.3560)	0.3188 (0.3257)	0.3063 (0.3098)
Morgenstern	0.4635 (0.1448)	0.3482 (0.1883)	0.3159 (0.3220)
𝑏=0.01
Normal (𝜌=0.5)	0.0084 (0.2778)	0.0491 (0.3115)	0.0645 (0.3211)
Normal (𝜌=0.85)	0.1224 (0.2216)	0.1370 (0.2191)	0.1401 (0.2186)
Studentt (𝜌=0.5)	0.3743 (0.3932)	0.3427 (0.3488)	0.3304 (0.3332)
Studentt (𝜌=0)	0.5787 (0.5957)	0.5913 (0.5986)	0.5739 (0.5772)
Logistic	0.3458 (0.3627)	0.3299 (0.3365)	0.3271 (0.3297)
A. Logistic	0.3499 (0.3652)	0.3362 (0.3419)	0.3257 (0.3285)
Morgenstern	0.4384 (0.1543)	0.3141 (0.2156)	0.2555 (0.2594)
𝑏=0.015
Normal (𝜌=0.5)	0.0031 (0.2862)	0.0579 (0.3185)	0.0733 (0.3285)
Normal (𝜌=0.85)	0.1272 (0.2244)	0.1419 (0.2229)	0.1460 (0.2237)
Studentt (𝜌=0.5)	0.3847 (0.4025)	0.3562 (0.3613)	0.3481 (0.3503)
Student t (𝜌=0)	0.5996 (0.6124)	0.6078 (0.6140)	0.5957 (0.5982)
Logistic	0.3558 (0.3715)	0.3451 (0.3505)	0.3433 (0.3453)
A. Logistic	0.3589 (0.3730)	0.3508 (0.3557)	0.3419 (0.3442)
Morgenstern	0.4209 (0.1616)	0.2949 (0.2300)	0.2399 (0.2721)