When I use regression models I feel leery of defaulting to an assumptions of linear association; instead I like to explore the functional form of relationships between dependent and explanatory variables using nonparametric smoothing regression (e.g. generalized additive models, lowess/lowess, running line smoothers, etc.) before estimating a parametric model using, as appropriate, nonlinear least squares regression to estimate parameters for functions suggested by the nonparametric model.
What is a good way to think about performing cross validation in the nonparametric smoothing regression phase of such an approach? I wonder if I might encounter a situation where in random holdout sample A a relationship approximated by a "broken stick" linear hinge function might be evident, while holdout sample B suggests a relationship that would be better approximated by a parabolic threshold hinge function.
Would one take a non-exhaustive approach hold back some randomly selected portion of the data, perform the nonparametric regression, interpret plausible functional forms for the result, and repeat this a few (human-manageable) number of times and mentally tally plausible functional forms?
Or would one take an exhaustive approach (e.g. LOOCV), and use some algorithm to 'smooth all the smooths' and used that smoothest of smooths to inform plausible functional forms? (Although, on reflection, I think LOOCV is quite unlikely to result in very different functional relationships since a functional form on a large enough sample is unlikely to be altered by a single data point.)
My applications will typically entail human-manageable numbers of predictor variables (a handful to a few dozen, say), but my sample sizes will range from from a few hundreds to a few hundred thousand. My aim is to produce an intuitively communicated and easily translated model that might be used to make predictions by people with data sets other than mine, and which do not include the outcome variables.
References in answers very welcome.