The Root-Unroot Algorithm for Density Estimation as Implemented via Wavelet Block Thresholding
Lawrence Brown, Tony Cai, Ren Zhang, Linda Zhao, and Harrison Zhou
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Abstract:
Density estimation has traditionally been treated separately from
nonparametric regression. In this paper we propose and implement a density
estimation procedure which begins by turning density estimation into a
regression problem. This regression problem is created by binning the
original observations into many small size bins, and by then applying
a suitable form of root transformation to the binned data counts. A
nonparametric regression estimator is then applied to the transformed
data. Finally, the estimated regression function is un-rooted by squaring
and normalizing.
In principle many common nonparametric regression estimators could be used in the implementation of this algorithm. We propose use of a wavelet block thresholding estimator. The entire algorithm is then convenient to implement. We show that the resulting density estimator enjoys a high degree of adaptivity. A numerical example and a practical data example are discussed to illustrate and explain the use of this density estimation procedure.
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- Other related papers:
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