Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferenti...

A distributed lag model (DLagM) is a regression model that includes lagged exposure variables as covariates; its corresponding distributed lag (DL) function describes the relationship between the lag and the coefficient of the lagged exposure variable. DLagMs have recently been used in environmental epidemiology for quantifying the cumulative effects of weather and air pollution on mortality an...

Single-index model is a potentially tool for multivariate nonparametric regression, generalizes both the generalized linear models(GLM) and the missing-link function problem in GLM. In this paper, we extend Cook’s local influence analysis to the penalized Gaussian likelihood estimator based on P-spline for the partially linear single-index model. Some influence measures, based on the minor pert...

Often, the functional form of covariate effects in an additive model varies across groups defined by levels of a categorical variable. This structure represents a factor-by-curve interaction. This article presents penalized spline models that incorporate factor-by-curve interactions into additive models. A mixed model formulation for penalized splines allows for straightforward model fitting an...

There exists a well known connection between penalized splines and mixed models. This connection makes it possible to exploit certain results derived for mixed models in the estimation of penalized splines. We have derived the Minimum Description Length (MDL) model selection criterion [1] for mixed models (see eg. [2]). In this paper we investigate the performance of the MDL criterion in fittin...

We construct bootstrap conndence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap conndence intervals are considered and compared. We nd that the commonly used bootstrap percentile intervals are inferior to the T intervals and to...

This paper develops Bayesian penalized spline predictive (BPSP) estimator of finite population proportion for probability-proportional-to-size samples. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior...