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 low-dimensional 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 multi-criterion 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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Cao, J., Ramsay, J.O. Parameter cascades and profiling in functional data analysis. Computational Statistics 22, 335–351 (2007). https://doi.org/10.1007/s00180-007-0044-1
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DOI: https://doi.org/10.1007/s00180-007-0044-1