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Transformations in density estimation. (With discussions). (English) Zbl 0742.62046
For the density estimation problem, the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this interesting article, followed by a comment by D. W. Scott and a rejoinder, the authors propose to transform the data with the intension that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the “back-transform” by change of variables of the global window width estimate of the transformed data’s density. They explore choosing the transformation from suitable parametric families. Data-based selection rules for the choice of transformations and the window width are discussed. Application to real and simulated data demonstrates the usefulness of their proposals.

62G07 Density estimation
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