Wavelet methods for curve estimation

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1340-1353
Journal / PublicationJournal of the American Statistical Association
Issue number428
Publication statusPublished - Dec 1994
Externally publishedYes


The theory of wavelets is a developing branch of mathematics with a wide range of potential applications. Compactly supported wavelets are particularly interesting because of their natural ability to represent data with intrinsically local properties. They are useful for the detection of edges and singularities in image and sound analysis and for data compression. But most of the wavelet-based procedures currently available do not explicitly account for the presence of noise in the data. A discussion of how this can be done in the setting of some simple nonparametric curve estimation problems is given. Wavelet analogies of some familiar kernel and orthogonal series estimators are introduced, and their finite sample and asymptotic properties are studied. We discover that there is a fundamental instability in the asymptotic variance of wavelet estimators caused by the lack of translation invariance of the wavelet transform. This is related to the properties of certain lacunary sequences. The practical consequences of this instability are assessed. © 1994 Taylor & Francis Group, LLC.

Research Area(s)

  • Delta sequences, Hazard rate, Kernel smoothing, Multiresolution analysis, Nonparametric regression, Orthogonal series

Bibliographic Note

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Citation Format(s)

Wavelet methods for curve estimation. / Antoniadis, A.; Gregoire, G.; McKeague, I. W.
In: Journal of the American Statistical Association, Vol. 89, No. 428, 12.1994, p. 1340-1353.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review