Functional principal component analysis (FPCA) is a dimension reduction technique that explains the dependence structure of a functional data set in terms of uncorrelated variables. In many applications the data are a set of smooth functions observed with error. In these cases the principal components are difficult to interpret because the estimated weight functions have a lot of variability an...

The paper discusses penalised spline (P -spline) smoothing for hazard regression of multivariable survival data. Non-proportional hazard functions are fitted in a numerically handy manner by employing Poisson regression which results from numerical integration of the cumulative hazard function. Multivariate smoothing parameters are selected by utilizing the connection between P -spline smoothin...

An obvious Bayesian nonparametric generalization of ridge regression assumes that coefficients are exchangeable, from a prior distribution of unknown form, which is given a Dirichlet process prior with a normal base measure. The purpose of this paper is to explore predictive performance of this generalization, which does not seem to have received any detailed attention, despite related applicat...

where μ(.) is an unknown smooth function, the i are independent and identically distributed errors, i.e. i ∼ (0, σ2 ), and the xi take values in [0, 1], for simplicity. We estimate μ(.) by some high dimensional spline of the form X(x)β + ZK(x)uK . Here, X(.) is a low dimensional basis while ZK(.) is built from truncated polynomials, i.e. we set X(x) = (1, x, x2/2!, . . . , xq/q!) and ZK(x) = ( ...

Estimation of monotone functions has broad applications in statistics, engineering, and science. This paper addresses asymptotic behaviors of monotone penalized spline estimators using constrained dynamical optimization techniques. The underlying regression function is approximated by a B-spline of an arbitrary degree subject to the first-order difference penalty. The optimality conditions for ...

Generalized additive models represented using penalized regression splines, estimated by penalized likelihood maximisation and with smoothness selected by generalized cross validation or similar criteria, provide a computationally efficient general framework for practical smooth modelling. Various authors have proposed approximate Bayesian interval estimates for such models, based on extensions...

We introduce an algorithm for reliably computing quantities associated with several types of semiparametric mixed models in situations where the condition number on the random effects matrix is large. The algorithm is numerically stable and efficient. It was designed to process penalized spline (P-spline) models without making unnecessary numerical approximations. The algorithm, PSQR (P-splines...

We propose a Bayesian Penalized Spline Predictive (BPSP) estimator for a finite population proportion in an unequal probability sampling setting. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of a population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior pre...