Transforms in Statistics

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).