Multiscale Variance Stabilization via Maximum Likelihood

This article proposes maximum likelihood approaches for multiscale variance stabilization (MVS) tranforms for independently and identically distributed data. For two MVS transforms we present new unified theoretical results on their Jacobians which are a key component of the likelihood. The new results provide (i) a deeper theoretical understanding of the transforms and (ii) the ability to compute the likelihood in linear time compared to previous numerical methods which required quadratic effort. The new MVS transforms are shown empirically to compare favourably to the well-known Box-Cox transform and almost dominate it. We show how the new transforms, like Box-Cox, can facilitate simpler models by an example involving the famous wool data.