Transforms in Statistics
No 2004,26, Papers from Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE)
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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