Estimating the Conditional Tail Expectation in the Case of Heavy-Tailed Losses

Table 2

Point estimates ${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$ and 95% confidence intervals for ${\mathrm{CTE}\hspace{0.17em}}_F(t)$ when $\gamma =3/4$.

$t=0.75$	$\text{CT}{\text{E}}_F(t)=9.719$
$n$	$k^{*}$	${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$	error	rmse	lower	upper	cover	length
$1000$	$051$	$9.543$	$0.018$	$0.582$	$8.589$	$9.543$	$0.854$	$0.954$
$2000$	$104$	$9.808$	$0.009$	$0.466$	$9.150$	$10.466$	$0.888$	$1.316$
$5000$	$222$	$9.789$	$0.007$	$0.410$	$9.363$	$10.215$	$0.915$	$0.852$
$t=0.90$	$\text{CT}{\text{E}}_F(t)=18.494$
$n$	$k^{*}$	${\widetilde{\mathrm{CTE}\hspace{0.17em}}}_n(t)$	error	rmse	lower	upper	cover	length
$1000$	$051$	$18.199$	$0.015$	$0.989$	$17.437$	$18.960$	$0.874$	$1.523$
$2000$	$104$	$18.696$	$0.011$	$0.858$	$18.052$	$19.340$	$0.895$	$1.288$
$5000$	$222$	$18.541$	$0.002$	$0.798$	$18.092$	$18.990$	$0.925$	$0.898$