On preconditioning the data for the wavelet transform when the sample size is not a power of two

A powerful and efficient method for nonparametric regression involves taking the discrete wavelet transform (DWT) of data, shrinking the resulting wavelet coefficients, and then computing the inverse wavelet transform to get an estimate of the regression function. Currently, most wavelet decomposition software packages require that the original set of data have sample size n equal to a power of two in order to achieve an exact orthogonal wavelet transform. In statistical data analysis, such is rarely the case, so in an effort to broaden the applicability of such methods, various ways of preconditioning data not meeting this restriction are discussed and compared.