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Transforms in Statistics

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Handbook of Computational Statistics

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Abstract

It is not an overstatement to say that statistics is based on various transformations of data. Basic statistical summaries such as the sample mean, variance, z-scores, histograms, etc., are all transformed data. Some more advanced summaries, such as principal components, periodograms, empirical characteristic functions, etc., are also examples of transformed data. To give a just coverage of transforms utilized in statistics will take a size of a monograph. In this chapter we will focus only on several important transforms with the emphasis on novel multiscale transforms (wavelet transforms and its relatives).

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Acknowledgements

Work on this chapter was supported by DOD/NSA Grant E-24-60R at Georgia Institute of Technology. Editor Jim Gentle read early versions of the chapter and gave many valuable comments. All matlab programs that produced figures and simulations are available from the author at request.

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Authors and Affiliations

  1. The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, 2101 Whitaker Building, 313 Ferst Drive, Atlanta, GA, 30332-0535, USA

    Brani Vidakovic

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  1. Brani Vidakovic
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Correspondence to Brani Vidakovic .

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Editors and Affiliations

  1. Dept. Computational & Data, Sciences, George Mason University, University Drive 4400, Fairfax, 22030-4444, Virginia, USA

    James E. Gentle

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. Dept. Socioinformation, Okayama University, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yuichi Mori

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Vidakovic, B. (2012). Transforms in Statistics. In: Gentle, J., Härdle, W., Mori, Y. (eds) Handbook of Computational Statistics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21551-3_8

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