POT-Based Estimation of the Renewal Function of Interoccurrence Times of Heavy-Tailed Risks

Table 1

Semiparametric and nonparametric estimates of the renewal function of interoccurrence times of Pareto-distributed claims with shape parameter 3/4. Simulations are repeated 200 times for different sample sizes.

True value $R=1.708$
Sample size	Semiparametric $\widehat{R}$			Nonparametric $\tilde{R}$
	Mean	Bias	RMSE	Mean	Bias	RMSE
$1000$	$1.696$	$-0.013$	$0.250$	$2.141$	$0.433$	$0.553$
$2000$	$1.719$	$0.011$	$0.183$	$1.908$	$0.199$	$0.288$
$5000$	$1.705$	$-0.003$	$0.119$	$1.686$	$-0.022$	$0.168$