Abramovich, F. and Bailey, T.C. and Sapatinas, T. (2000) Wavelet analysis and its statistical applications. Journal of the Royal Statistical Society Series D-the Statistician, 49 (1). pp. 1-29. ISSN 0039-0526.
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In recent years there has been a considerable development in the use of wavelet methods in statistics. As a result, we are now at the stage where ii is reasonable to consider such methods to be another standard tool of the applied statistician rather than a research novelty. With that in mind, this paper gives a relatively accessible introduction to standard wavelet analysis and provides a review of some common uses of wavelet methods in statistical applications. It is primarily orientated towards the general statistical audience who may be involved in analysing data where the use of wavelets might be effective, rather than to researchers who are already familiar with the field. Given that objective, we do not emphasize mathematical generality or rigour in our exposition of wavelets and we restrict our discussion to the more frequently employed wavelet methods in statistics. We provide extensive references where the ideas and concepts discussed can be followed up in greater detail and generality ii required. The paper first establishes some necessary basic mathematical background and terminology relating to wavelets. It then reviews the more well-established applications of wavelets in statistics including their use in nonparametric regression, density estimation, inverse problems, changepoint problems and in some specialized aspects of time series analysis. Possible extensions to the uses of wavelets in statistics are then considered. The paper concludes with a brief reference to readily available software packages for wavelet analysis.
|Uncontrolled keywords:||changepoint analysis; density estimation; Fourier analysis; inverse problems; nonparametric regression; signal processing; spectral density estimation; time series analysis; wavelet analysis|
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Suzanne Duffy|
|Date Deposited:||25 Aug 2009 11:29|
|Last Modified:||25 Aug 2009 11:29|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/16040 (The current URI for this page, for reference purposes)|
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