Variance Stabilizing Transformations for Intensity Estimators of Shot Noise

This letter considers two estimators of the intensity
$\lambda$
of the Shot Noise process for high values of
$\lambda$
. They are based on the first and the second empirical cumulants of the Shot Noise. For both statistics, it is shown that their respective variance grows respectively linearly and quadratically with
$\lambda$
. We construct Variance Stabilizing Transforms (and their corresponding inverse transforms) for both estimators thanks to the Delta method so as to make their respective variance constant (regardless of
$\lambda$
). Asymptotic distributions of the variance stabilized estimators are established. Finally, variance stabilization property is validated by Monte-Carlo simulations.