Simulations show that our approach is competitive to existing approaches in the piecewise-constant low intensity setting and outperforms them for moderate and high intensities. Like existing approaches cycle-shifting can dramatically improve the performance of our method. Other simulations show that our method significantly outperforms existing wavelet methods when estimating smoothly changing intensities where the number of competitors is limited.
We apply our technique to the estimation of the intensity of the well-known earthquake data. Our method can simultaneously detect small peaks but not oversmooth large peaks. We point out that our method can be easily extended to higher dimensions. {\em Keywords:} Poisson process, variance stabilizing transform, transform to normal, cycle-shifting.