TY - JOUR

T1 - A multiscale variance stabilization for binomial sequence proportion estimation

AU - Nunes, Matthew A.

AU - Nason, Guy P.

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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.

KW - Binomial random variable

KW - Gaussianization

KW - Haar-Fisz

KW - sequence probability estimation

KW - variance stabilization

KW - GENERALIZED LINEAR-MODELS

KW - WAVELET SHRINKAGE

KW - BANDWIDTH SELECTION

KW - SPATIAL ADAPTATION

KW - REGRESSION

KW - INTENSITY

KW - ISOCHORES

M3 - Journal article

VL - 19

SP - 1491

EP - 1510

JO - Statistica Sinica

JF - Statistica Sinica

SN - 1017-0405

IS - 4

ER -