Poisson Intensity Estimation Using Wavelets and the

This article introduces a new method for the estimation of the intensity of an inhomogeneous one-dimensional Poisson process. The Fisz transformation transforms a vector of binned Poisson counts to approximate normality. Theory shows that, asymptotically, the transformed vector is normal and the elements uncorrelated. Hence we can use wavelet shrinkage with a global threshold to estimate the Poisson intensity. 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 signiicantly 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.