We propose a new small area estimation approach that combines small area random effects with a smooth, nonparametrically specified trend. By using penalized splines as the representation for the nonparametric trend, it is possible to express the small area estimation problem as a mixed effect regression model. We show how this model can be fitted using existing model fitting approaches such as ...

In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric est...

We consider the problem of estimating a smooth function from noisy, sampled data. We use orthonormal bases of compactly supported wavelets to constriuct nonlinear function estimates which can significantly outperform evey linear method (kernel, smoothing spline, sieve, ...). Our estimates are simple nonlinear functions of the empirical wavelet coefficients and are asymptotically minimax over ce...

We thank Hansen and Kooperberg (HK) for an interesting paper discussing model selection methods in the context of Extended Linear Models. We comment on their univariate density estimation studies, which maximize the log likelihood in a low dimensional linear space. They consider spline bases for this space and consider greedy and Bayesian methods for choosing the knots. We describe a penalized ...

BACKGROUND Smoothing methods are widely used to analyze epidemiologic data, particularly in the area of environmental health where non-linear relationships are not uncommon. This study focused on three different smoothing methods in Cox models: penalized splines, restricted cubic splines and fractional polynomials. OBJECTIVES The aim of this study was to assess the effects of prognostic facto...

Little and An (2004, Statistica Sinica 14, 949-968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covar...

Nonparametric regression modelling has received considerable attention and many methods have been proposed to draw information from data with complex structure. We consider the use of B-spline nonparametric regression models estimated by penalized likelihood methods. A crucial point in constructing the models is in the choice of a smoothing parameter and the number of knots, for which several a...

A general methodology for modeling loss data depending on covariates is developed. The parameters of the frequency and severity distributions of the losses may depend on covariates. The loss frequency over time is modeled via a non-homogeneous Poisson process with integrated rate function depending on the covariates. This corresponds to a generalized additive model which can be estimated with s...

A new methodology is proposed for estimating the proportion of true null hypotheses in a large collection of tests. The proportion of true null hypotheses is needed, for example, when controlling the false discovery rate in the analysis of microarray data. We assume that each test concerns a single parameter δ whose value is specified by the null hypothesis. Our methodology combines a parametri...