Wavelet-based Functional Mixed Models

• DOI: 10.1111/j.1467-9868.2006.00539.x
• Publication Date: 2006-03-03T15:10:01Z
• Authors: Jeffrey S. Morris; Raymond J. Carroll
• Keywords: Mixed model; Pointwise

Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and observed data consist sets that sampled on a fine grid. We present new methodology generalizes linear mixed model to framework, with fitting done by using Bayesian wavelet-based approach. This method is flexible, allowing functions arbitrary form full range fixed effects structures between-curve covariance available framework. It yields nonparametric estimates random-effects as well various within-curve matrices. The adaptively regularized result non-linear shrinkage prior imposed effects' wavelet coefficients, random-effect experience adaptive regularization because separately estimated variance components for each coefficient. Because we have posterior samples all quantities, can perform pointwise or joint inference prediction quantities model. adaptiveness makes it especially appropriate modelling irregular characterized numerous local features like peaks.