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

Table 2

Semiparametric and nonparametric estimates of the renewal function of interoccurence times of Pareto-distributed claims with shape parameter 2/3. Simulations are repeated 200 times for different sample sizes.

True value $R=2.222$
Sample size	Semiparametric $\widehat{R}$			Nonparametric $\tilde{R}$
	Mean	Bias	RMSE	Mean	Bias	RMSE
$1000$	$2.265$	$0.042$	$0.185$	$2.416$	$0.193$	$0.229$
$2000$	$2.247$	$0.024$	$0.157$	$2.054$	$-0.167$	$0.223$
$5000$	$2.223$	$0.001$	$0.129$	$2.073$	$-0.149$	$0.192$