Extended Linear Modeling with Splines: a Unifying Paradigm

Statistical modeling with splines has been studied in a number of
contexts: regression, logistic regression, density estimation, hazard
estimation, and so forth. From a methodological perspective these
contexts are considerably different. At least, no one has bothered
to develop an algorithm that handles all of them. From a
theoretical perspective, however, these and several other contexts
can be treated simultaneously as special cases of concave extended
linear modeling. The resulting theory applies to ANOVA modeling and also
to free knot as well as fixed knot splines. Here we discuss
this general theory and give two fresh applications:
(i) estimating the dependence of the drift of a diffusion process with
jumps on a vector of time-dependent covariates; (ii) robust regression
corresponding to least absolute value residuals or more general M-estimates.
(Jianhua Huang has been involved in much of the recent underlying research.)