### 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.

Original language | English |
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Pages (from-to) | 1491-1510 |

Number of pages | 20 |

Journal | Statistica Sinica |

Volume | 19 |

Issue number | 4 |

Publication status | Published - 1 Oct 2009 |

### Keywords

- Binomial random variable, Gaussianization, Haar-Fisz, sequence probability estimation, variance stabilization, GENERALIZED LINEAR-MODELS, WAVELET SHRINKAGE, BANDWIDTH SELECTION, SPATIAL ADAPTATION, REGRESSION, INTENSITY, ISOCHORES

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## Cite this

Nunes, M. A., & Nason, G. P. (2009). A multiscale variance stabilization for binomial sequence proportion estimation.

*Statistica Sinica*,*19*(4), 1491-1510. http://www3.stat.sinica.edu.tw/statistica/j19n4/j19n48/j19n48.html