A multiscale variance stabilization for binomial sequence proportion estimation

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. We also explore the efficacy of our method in real applications.