Authors: Jiguo Cao James O Ramsay
Publish Date: 2007/03/28
Volume: 22, Issue: 3, Pages: 335-351
Abstract
A data smoothing method is described where the roughness penalty depends on a parameter that must be estimated from the data Three levels of parameters are involved in this situation Local parameters are the coefficients of the basis function expansion defining the smooth global parameters define lowdimensional trend and the roughness penalty and a complexity parameter controls the amount of roughness in the smooth By defining local parameters as regularized functions of global parameters and global parameters in turn as functions of complexity parameter we define a parameter cascade and show that the accompanying multicriterion optimization problem leads to good estimates of all levels of parameters and their precisions The approach is illustrated with real and simulated data and this application is a prototype for a wide range of problems involving nuisance or local parameters
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