Statistica Sinica

Matthew A. Nunes and Guy P. Nason

Abstract:There exist many different wavelet methods for classical nonparametric regression in the statistical literature. However, techniques specifically designed for binomial intensity estimation are relatively uncommon. In this article, we propose a new technique for the estimation of the proportion of a binomial process. This method, called the Haar-NN transformation, transforms the data to be approximately normal with constant variance. This reduces the binomial proportion problem to the usual `function plus normal noise' regression model and thus any wavelet denoising method can be used for the intensity estimation. We demonstrate that our methodology possesses good Gaussianization and variance-stabilizing properties through extensive simulations, comparing it to traditional transformations. Further, we show that cycle-spinning can improve the performance of our technique. We also explore the efficacy of our method in an application.

Key words and phrases:Binomial random variable, Gaussianization, Haar-Fisz, sequence probability estimation, variance stabilization.