This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and...

Given spatially located observed random variables (x; z) = f(x i ; z i)g i , we propose a new method for nonparametric estimation of the potential functions of a Markov Random Field p(xjz), based on a roughness penalty approach. The new estimator maximises the penalized log-pseudolikelihood function and is a natural cubic spline. The calculations involved do not rely on Monte Carlo simulation. ...

Spaces of polynomial splines deened on planar triangulations are very useful tools for tting scattered data in the plane. Recently, 4, 5], using homogeneous polynomials, we have developed analogous spline spaces deened on triangulations on the sphere and on sphere-like surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and tting methods. Her...

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus ...

We describe the use of smoothing spline analysis of variance (SSANOVA) in the penalized log likelihood context, for learning (estimating) the probability p of a '1' outcome, given a training set with attribute vectors and outcomes. p is of the form pet) = eJ(t) /(1 + eJ(t)), where, if t is a vector of attributes, f is learned as a sum of smooth functions of one attribute plus a sum of smooth fu...

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus ...

Spaces of polynomial splines deened on planar triangulations are very useful tools for tting scattered data in the plane. Recently, 4, 5], using homogeneous polynomials, we have developed analogous spline spaces deened on triangulations on the sphere and on sphere-like surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and tting methods. Her...

In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other cova...

We propose extensions of penalized spline generalized additive models for analysing space-time regression data and study them from a Bayesian perspective. Non-linear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatial effects follow a Markov random field prior. This allows to treat all functions and effects withi...

We propose extensions of penalized spline generalized additive models for analyzing space-time regression data and study them from a Bayesian perspective. Non-linear effects of continuous covariates and time trends are modelled through Bayesian versions of penalized splines, while correlated spatial effects follow a Markov random field prior. This allows to treat all functions and effects withi...