Penalized B-splines are commonly used in additive models to describe smooth changes in a response with quantitative covariates. This is usually done through the conditional mean in the exponential family using generalized additive models with an indirect impact on other conditional moments. Another common strategy is to focus on several low-order conditional moments, leaving the full 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. The latter proposal for a right- or interval-censored continuous response with a highly flexible and smooth nonparametric density is considered. The focus is on location-scale models with additive terms in the conditional mean and standard deviation. Starting from recent results in the Bayesian framework, a fast converging algorithm is proposed to select penalty parameters from their marginal posteriors. It is based on Laplace approximations of the conditional posterior of the spline parameters. Simulations suggest that the estimators obtained in this way have excellent frequentist properties and superior efficiencies compared to approaches with a working Gaussian assumption. The methodology is illustrated by the analysis of right- and interval-censored income data.

惩罚性B样条曲线通常用于加性模型中，以描述带有定量协变量的响应中的平滑变化。这通常是通过使用广义加性模型通过指数族中的条件均值来完成的，而该模型会间接影响其他条件矩。另一个常见的策略是关注几个低阶条件矩，而未指定完整的条件分布。替代地，可以假定响应的多参数分布，其中一些参数使用加法表达式在协变量上共同回归。考虑到后者的建议，即具有高度灵活和平滑的非参数密度的右删减或连续删减的连续响应。重点是在条件均值和标准差中具有加法项的位置比例模型。从贝叶斯框架的最新结果开始，提出了一种快速收敛算法，以从其边际后验中选择惩罚参数。它基于样条参数的条件后验的Laplace近似。仿真表明，与采用工作高斯假设的方法相比，以这种方式获得的估计量具有出色的频度特性和出色的效率。该方法通过对权利和间隔检查的收入数据进行分析来说明。仿真表明，与采用工作高斯假设的方法相比，以这种方式获得的估计量具有出色的频度特性和出色的效率。该方法通过对权利和间隔检查的收入数据进行分析来说明。仿真表明，与采用工作高斯假设的方法相比，以这种方式获得的估计量具有出色的频度特性和出色的效率。该方法通过对权利和间隔检查的收入数据进行分析来说明。