In this chapter, the problem of ridge estimation is studied in the context of partially linear models (PLMs). In a nutshell, PLMs are smoothed models that include both parametric and nonparametric parts. They allow more flexibility compared to full/nonparametric regression models.
Consider the usual PLM with the form
where is a vector of explanatory variables, is an unknown ‐dimensional parameter vector, the 's are known and nonrandom in some bounded domain , is an unknown smooth function, and 's are i.i.d. random errors with mean 0, variance , which are independent of . PLMs are more flexible than standard linear models since they ...