  Penalized B-splines are routinely used in additive models to describe smooth
changes in a response with quantitative covariates. It is typically done
through the conditional mean in the exponential family using generalized
additive models with an indirect impact on other conditional moments. Another
common strategy consists in focussing on several low-order conditional moments,
leaving the complete conditional distribution unspecified. Alternatively, a
multi-parameter distribution could be assumed for the response with several of
its parameters jointly regressed on covariates using additive expressions.
  Our work can be connected to the latter proposal for a right- or
interval-censored continuous response with a highly flexible and smooth
nonparametric density. We focus on location-scale models with additive terms in
the conditional mean and standard deviation. Starting from recent results in
the Bayesian framework, we propose a quickly converging algorithm to select
penalty parameters from their marginal posteriors. It relies on Laplace
approximations to the conditional posterior of the spline parameters.
Simulations suggest that the so-obtained estimators own excellent frequentist
properties and increase efficiency as compared to approaches with a working
Gaussian hypothesis. We illustrate the methodology with the analysis of
imprecisely measured income data.
