In this chapter we gave an overview of several transforms useful in computational statistics. We emphasized frequency and scale domain transforms (Fourier and wavelet) since they provide an insight to the phenomena, not available in the domain of untransformed data. Moreover, multiscale transforms are relatively new, and as such deserve more attention. It was pretentious to title this chapter Transforms in Statistics, since literally several dozens important transforms are not even mentioned. As it was hinted in the introduction, a just task of overviewing all important transformations used in statistical practice would take a space of a large monograph.
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.