Title: Nonparametric location-scale models for right- and interval-censored data with inference based on Laplace approximations.
Abstract: A double additive model for the conditional mean and standard
deviation in location-scale models with a nonparametric error distribution is proposed. The response is assumed continuous and possibly subject to right or interval-censoring. Nonparametric inference from censored data in location-scale models has been studied by many authors, but it generally focuses on the estimation of conditional location and can only deal with the estimation of the smooth effects of a very limited number of covariates. Additive models based on P-splines are preferred here for their excellent properties and the possibility to handle a large number of additive terms (Eilers and Marx 2002). They are used to specify the joint effect of covariates on location and dispersion within the location-scale model. A nonparametric error distribution with a smooth underlying hazard function and fixed moments is assumed for the standardized error term. In the absence of right-censoring, a location-scale model with a small number of additive terms and a quartile-constrained error density (instead of the hazard here) was considered in Lambert (2013) to analyse interval-censored data, with inference relying on a numerically demanding MCMC algorithm. It is shown how Laplace approximations to the conditional posterior of spline parameters can be combined to bring fast and reliable estimation of the linear and additive terms, and provide a smooth estimate of the underlying error hazard function under moment constraints. These approximations are the cornerstones in the derivation of the marginal posteriors for the penalty parameters and smoothness selection. The resulting estimation procedures are motivated using Bayesian arguments and shown to own excellent frequentist properties. They are extremely fast and can handle a large number of additive terms within a few seconds even with pure R code. The methodology is illustrated with the analysis of right- and interval-censored income data in a survey.