2020/05/11 by Philippe Lambert, Lambert, Philippe
Mathematics · #Advanced Causal Inference Techniques #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2005.05156
openalex publication_date 2020/05/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Penalized B-splines are routinely used in additive models to describe smooth\nchanges in a response with quantitative covariates. It is typically done\nthrough the conditional mean in the exponential family using generalized\nadditive models with an indirect impact on other conditional moments. Another\ncommon strategy consists in focussing on several low-order conditional moments,\nleaving the complete conditional distribution unspecified. Alternatively, a\nmulti-parameter distribution could be assumed for the response with several of\nits parameters jointly regressed on covariates using additive expressions.\n Our work can be connected to the latter proposal for a right- or\ninterval-censored continuous response with a highly flexible and smooth\nnonparametric density. We focus on location-scale models with additive terms in\nthe conditional mean and standard deviation. Starting from recent results in\nthe Bayesian framework, we propose a quickly converging algorithm to select\npenalty parameters from their marginal posteriors. It relies on Laplace\napproximations to the conditional posterior of the spline parameters.\nSimulations suggest that the so-obtained estimators own excellent frequentist\nproperties and increase efficiency as compared to approaches with a working\nGaussian hypothesis. We illustrate the methodology with the analysis of\nimprecisely measured income data.\n