A note on design transformation and binning in nonparametric curve estimation

Peter Hall, Byeong U. Park, Berwin A. Turlach

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Methods based on design transformation and equal-number binning are shown to overcome problems of design sparseness, while retaining excellent theoretical properties. In company with local linear smoothing they produce optimal estimators, although with optimality defined a little differently from in the nontransformed case. When used in conjunction with wavelet techniques they overcome problems of stochastic design, but, unlike related techniques based on convolution and interpolation, do not degrade features of the signal through prior smoothing, or inflate the variance. Density estimation; Local linear smoothing; Mean squared error; Nonparametric regression; Wavelets.

Original languageEnglish
Pages (from-to)469-476
Number of pages8
Issue number2
Publication statusPublished - 1998
Externally publishedYes


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